Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.4 - The Chain Rule - 3.4 Exercises: 61

Answer

$$F'(5)=24$$

Work Step by Step

$$F(x)=f(g(x))$$ Apply the Chain Rule, we have $$F'(x)=\frac{d[f(g(x))]}{d[g(x)]}\frac{d[g(x)]}{dx}$$ $$F'(x)=f'(g(x))\times g'(x)$$ Therefore, $$F'(5)=f'(g(5))\times g'(5)$$ We have $g(5)=-2$ and $g'(5)=6$. So, $$F'(5)=f'(-2)\times6$$ We also have $f'(-2)=4$. Therefore, $$F'(5)=4\times6=24$$
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