How do you differentiate #f(x)= (1-3x^2)^4* (1-x+7x^2)^4 # using the product rule?
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1To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
1.To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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IdentifyTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 )To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify theTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) usingTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the twoTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functionsTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product ruleTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multipliedTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, followTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these stepsTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
- Identify the two functions being multiplied: ( u(x) = (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
1.To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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IdentifyTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 -To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the twoTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functionsTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions beingTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multipliedTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied togetherTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together:To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: (To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( uTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) andTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) =To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( vTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) =To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 \To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 -To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
2To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x +To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
2.To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
ApplyTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the productTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product ruleTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, whichTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which statesTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states thatTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivativeTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ). 2To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative ofTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
ApplyTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the productTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the productTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product ofTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product ruleTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of twoTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule:To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functionsTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions isTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)'To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative ofTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' =To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = uTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the firstTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first functionTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'vTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uvTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the secondTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv'To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second functionTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plusTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ). To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ). 3.To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first functionTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
DifferentTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function timesTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( uTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivativeTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative ofTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) )To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) withTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the secondTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respectTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second functionTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect toTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
3To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
3.To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x )To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) toTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivativesTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to findTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives ofTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of (To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( uTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x)To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) \To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ). 4To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) )To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ). 4.To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) andTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
DifferentTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( vTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( vTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) \To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x)To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separatelyTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using theTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respectTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain ruleTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
4To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x )To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
DerTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) toTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative ofTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to findTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of (To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( uTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( vTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x)To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) \To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x)To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ):To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ). 5To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): \To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ). 5.To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
SubstituteTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ uTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( uTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x)To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x)To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ),To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x)To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ),To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), (To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x)To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdotTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ),To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), andTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) \To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
5To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(xTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x)To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ fTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) intoTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the productTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product ruleTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) =To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formulaTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula. To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
SimplTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)vTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
SimplifyTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
Simplify the resultTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(x)To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
Simplify the result to obtain the derivative ofTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(x) +To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
Simplify the result to obtain the derivative of ( fTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(x) + uTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
Simplify the result to obtain the derivative of ( f(x)To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(x) + u(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
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Simplify the result to obtain the derivative of ( f(x) ) withTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
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Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
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Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
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Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
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Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
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Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
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Apply the product rule formula: [ f'(x) = u'(x)v(x) + u(x)vTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
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Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
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Apply the product rule: ( (uv)' = u'v + uv' ).
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Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
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Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
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Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
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Simplify the result to obtain the derivative of ( f(x) ) with respect toTo differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(x) + u(x)v'(To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
Simplify the result to obtain the derivative of ( f(x) ) with respect to ( x \To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(x) + u(x)v'(xTo differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
Simplify the result to obtain the derivative of ( f(x) ) with respect to ( x ).To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(x) + u(x)v'(x)To differentiate ( f(x) = (1 - 3x^2)^4 \cdot (1 - x + 7x^2)^4 ) using the product rule:
-
Identify the two functions being multiplied: ( u(x) = (1 - 3x^2)^4 ) and ( v(x) = (1 - x + 7x^2)^4 ).
-
Apply the product rule: ( (uv)' = u'v + uv' ).
-
Differentiate ( u(x) ) with respect to ( x ) to find ( u'(x) ).
-
Differentiate ( v(x) ) with respect to ( x ) to find ( v'(x) ).
-
Substitute ( u(x) ), ( v(x) ), ( u'(x) ), and ( v'(x) ) into the product rule formula.
-
Simplify the result to obtain the derivative of ( f(x) ) with respect to ( x ).To differentiate the function ( f(x) = (1-3x^2)^4 \cdot (1-x+7x^2)^4 ) using the product rule, follow these steps:
-
Identify the two functions being multiplied together: ( u(x) = (1-3x^2)^4 ) and ( v(x) = (1-x+7x^2)^4 ).
-
Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
-
Calculate the derivatives of ( u(x) ) and ( v(x) ) separately using the chain rule.
-
Derivative of ( u(x) ): [ u'(x) = 4(1-3x^2)^3 \cdot (-6x) ]
-
Derivative of ( v(x) ): [ v'(x) = 4(1-x+7x^2)^3 \cdot (-1+14x) ]
-
Apply the product rule formula: [ f'(x) = u'(x)v(x) + u(x)v'(x) ]
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Substitute the derivatives and original functions into the formula: [ f'(x) = (4(1-3x^2)^3 \cdot (-6x))(1-x+7x^2)^4 + (1-3x^2)^4(4(1-x+7x^2)^3 \cdot (-1+14x)) ]
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Simplify the expression if necessary.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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