Determine the derivative of (f∘g)(x) where f(x)=x2−6x−4 and g(x)=−3x2−2x−7.

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Lesson Parent: 
The Chain Rule
Problem: 

Determine the derivative of (f∘g)(x) where f(x)=x2−6x−4 and g(x)=−3x2−2x−7.

Answer: 

(f∘g)′(x)=f′(g(x))g′(x)=36x3+36x2+128x+40

SAMPLE SOLUTION

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Solution: 

Recall our lessons on function composition and the Chain Rule.

First let's find f'(x) and g'(x). We know what the derivative of a polynomial is. This gives

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and

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Therefore, the composition

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And finally,

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