Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.2 Inverse Functions - Exercises - Page 335: 27


$$g'(x)= -\frac{1}{5x^{6/5}} .$$

Work Step by Step

Since $f(x)=x^{-5}$, then $f'(x)=-5x^{-6}$. Hence by Theorem 2 and assuming that $g(x)=f^{-1}(x)$, we have $$g(x)= x^{-1/5}, \quad g'(x)=\frac{1}{f'(g(x))}=-\frac{1}{5x^{6/5}} .$$
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