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Asked Dec 5, 2019
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Use the product rule to find the derivative of a function in the form f(x)g(x)h(x)
Question
For k(x) = (3x² + 3x – 2)(2x – 1)(-2x), find the derivative of k(x) at the point x = 0 using the product rule.
Do not include "k' (x) =" in your answer. For example, if your answer is k'(x) = 4, you would enter 4.
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Use the product rule to find the derivative of a function in the form f(x)g(x)h(x) Question For k(x) = (3x² + 3x – 2)(2x – 1)(-2x), find the derivative of k(x) at the point x = 0 using the product rule. Do not include "k' (x) =" in your answer. For example, if your answer is k'(x) = 4, you would enter 4.

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Expert Answer

Step 1

Given:

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k(x) =(3x² + 3x + 2)(2x – 1)(-2x)

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Step 2

Concept used:

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Product rule: S.8)=(S)(8)+(8) f•8)=( dx dx dx

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Step 3

Differentiate k (x) with respect ‘x&r...

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:+2)(2x – 1)(-2x) k (x)=(3x² +3x +2)(-4x² + 2x) k(x)=(3x² +3x +2 k'(x) =(3x² +3x + 2)(-4x° + 2x)+(-4x° + 2x)(3x* + 3x k'(x)=(3x² +3x + 2)·-(2(-4)x+ 2) +(-4x² + 2.x) (2·3x +3) k'(x) = (3x² + 3x + 2)•(-&r + 2) +(-4x² + 2x) (6xr + 3) k' (x) =-24x² – 24x² –16x+ 6x² +6x +4– 24x +12.x² -12x +6x de k' (x) =-48x² – 18.r – 4x + 4

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