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