Determine the derivative of (f∘g)(x) where f(x)=−2x2+x+2 and g(x)=2x2+2x−2.

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Lesson Parent: 
The Chain Rule
Problem: 

Determine the derivative of (f∘g)(x) where f(x)=−2x2+x+2 and g(x)=2x2+2x−2.

Answer: 

(f∘g)′(x)=f′(g(x))g′(x)=−32x3−48x2+20x+18

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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