How do you find the derivative of #f(x)=5(-3x^2+5x+1)#?
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To find the derivative of ( f(x) = 5(-3x^2 + 5x + 1) ), you can use the power rule and constant multiple rule. Here's the step-by-step process:
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Use the constant multiple rule: Multiply the constant (5) by the derivative of the expression inside the parentheses. [ f'(x) = 5 \cdot \frac{d}{dx}(-3x^2 + 5x + 1) ]
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Find the derivative of each term inside the parentheses using the power rule: [ \frac{d}{dx}(-3x^2 + 5x + 1) = -6x + 5 ]
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Substitute the derivative back into the equation: [ f'(x) = 5(-6x + 5) ]
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Distribute the constant (5) to each term inside the parentheses: [ f'(x) = -30x + 25 ]
So, the derivative of ( f(x) = 5(-3x^2 + 5x + 1) ) is ( f'(x) = -30x + 25 ).
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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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