Single Variable Calculus, Chapter 7, 7.7, Section 7.7, Problem 32

Determine the derivative of $g(x) = \cos h (\ln x)$. Simplify where possible.


$
\begin{equation}
\begin{aligned}

g'(x) =& \frac{d}{dx} \cos h (\ln x)
\\
\\
g'(x) =& \sin h (\ln x) \cdot \frac{d}{dx} (\ln x)
\\
\\
g'(x) =& \sin h (\ln x) \cdot \frac{1}{x}
\\
\\
g'(x) =& \frac{\sin h (\ln x)}{x}

\end{aligned}
\end{equation}
$