University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.8 - Derivatives of Inverse Functions and Logarithms - Exercises - Page 175: 97

Answer

$\frac{d(gof)(x)}{dx}=\frac{1}{\frac{df(x)}{dx}}$

Work Step by Step

The given function is: $(gof)(x)=x$ on differentiating both sides: $\frac{d(gof)(x)}{dx}\times\frac{df(x)}{dx}=\frac{dx}{dx}$ $\frac{d(gof)(x)}{dx}=\frac{1}{\frac{df(x)}{dx}}$
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