\documentclass[12pt]{exam}
\noprintanswers
\noaddpoints

\usepackage{amsmath}
\usepackage{graphicx,float}
\usepackage{wrapfig}
\usepackage{enumerate}

\usepackage{tikz}
\usepackage{pgfplots}


\begin{document}

\begin{questions}

\question 

\begin{parts}

\part Construct a function $f(x)$ for which you \emph{must} use logarithmic differentiation to compute $f'(x)$. Then compute $f'(x)$.

\part Construct a function $g(x)$ for which $\ln(g(x)) = \frac{\ln(x)}{2} + x\ln(\cos(x))$. Compute $g'(x)$.
% g(x) = \sqrt{x}*\cos(x)^x
% g'(x) / g(x) =  1/(2x) + \ln(\cos(x)) - x \tan(x)
% g'(x) = ( 1/(2x) + \ln(\cos(x)) - x \tan(x) ) \sqrt{x}*\cos(x)^x

\part Suppose that $h_1(x)$ and $h_2(x)$ are two functions so that $\ln(h_1(x)) = \ln(h_2(x)) + 1$. What is the relationship between $h_1'(x)$ and $h_2'(x)$?
% h_1(x) = e * h_2(x)
% so h_1'(x) = e * h_2'(x)

\end{parts}

\end{questions}

\end{document}

