Calculus 10th Edition

$h'(x)=-\dfrac{1}{x^2}-12\sec(x)\tan(x)$.
$h(x)=f(x)+g(x)\rightarrow f(x)=\dfrac{1}{x}$; $g(x)=-12\sec(x)$. 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: $h'(x)=f'(x)+g'(x)=-\dfrac{1}{x^2}-12\sec(x)\tan(x)$.