Answer
$h'(x)=-\dfrac{1}{x^2}-12\sec(x)\tan(x)$.
Work Step by Step
$h(x)=f(x)+g(x)\rightarrow f(x)=\dfrac{1}{x}$; $g(x)=-12\sec(x)$.
Using the Power Rule: $f'(x)=(-1)(x^{-1-1})=-\dfrac{1}{x^2}$.
By Theorem 2.9 and the Constant Multiple Rule:
$g'(x)=-12(\dfrac{d}{dx}\sec(x))=-12\sec(x)\tan(x)$.
Using the Sum Rule:
$h'(x)=f'(x)+g'(x)=-\dfrac{1}{x^2}-12\sec(x)\tan(x)$.
