# Chapter 2 - Differentiation - 2.3 Exercises - Page 125: 43

$f'(x)=-1+\sec^2(x)$.

#### Work Step by Step

$f(x)=g(x)+h(x)\rightarrow g(x)=-x$ and $h(x)=\tan(x)$. Using the Power Rule: $g'(x)=-1$. By Theorem $2.9$: $\frac{d}{dx}(\tan(x))=\sec^2(x)$. Using the Sum Rule $f'(x)=g'(x)+h'(x)$. $f'(x)=-1+\sec^2(x)$

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