How do you find the first and second derivatives of #y=(2x^4-3x)/(4x-1)# using the quotient rule?
First Derivative:
Second Derivative:
First, I'll introduce the quotient rule.
Getting the first derivative:
Use the quotient rule.
Simplify.
Getting the second derivative:
Use the quotient rule.
Simplify.
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To find the first and second derivatives of the given function ( y = \frac{2x^4 - 3x}{4x - 1} ) using the quotient rule:
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First derivative: [ y' = \frac{(4x - 1)(8x^3) - (2x^4 - 3x)(4)}{(4x - 1)^2} ]
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Second derivative: [ y'' = \frac{(4x - 1)^2(24x^2) - (4x - 1)(8x^3) - (2x^4 - 3x)(4)}{(4x - 1)^4} ]
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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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