Answer
See proof
Work Step by Step
Differentiate both sides of the given equation $f(g(x))=x$:
$$g'(x)f'(g(x))=1$$
$$g'(x)(1+[f(g(x))]^{2}=1$$
$$g'(x)(1+x^{2})=1$$
$$g'(x)=\frac{1}{(1+x^{2})}$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 2 - Derivatives - Review - Exercises - Page 199: 90
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