## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 146: 25

#### Answer

$$f'(g(x))= \sec^2 x-\csc^2x$$

#### Work Step by Step

Given $$f(u)=u+u^{-1}, \quad g(x)=\tan x$$ Since \begin{align*} f(g(x))&=\tan x+ (\tan x)^{-1}\\ &= \tan x+ \cot x \end{align*} Then $$f'(g(x))= \sec^2 x-\csc^2x$$

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