## Calculus 10th Edition

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