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\begin{document}
\begin{center}

\Huge{Exponential Derivatives}\\
\end{center}

\normalsize

\begin{enumerate}
\item For each $f$ defined below, find $f'(x)$.

$f(x)=x^4+2e^x$  \hspace{1in} $f(x)=e^{x+4}-7e^2$  \hspace{1in} $\displaystyle{f(x)=\frac{e^x+7}{e}}$

\vspace{2in}

\item Consider $\alpha(x)=x^4+2e^x$.
\begin{enumerate}
\item Find the equation of the line tangent to the graph of $\alpha$ at the point $(0,2)$.
\vskip 2in
\item Find the line normal the the line you found in part (a) that also passes through the point $(0,2)$.
\vskip 1in
\end{enumerate}
 
 
 \item At what point on the curve of $y=1+2e^x-3x$ is the tangent line parallel to the line $3x-y=5$?
 \vskip 2in
 \end{enumerate}
\newpage

\begin{center}
\Huge{Trigonometric Derivatives}\\
\end{center}

\begin{enumerate}
\item For each $f$ defined below, find $f'(x)$.

$f(x)=\sin(x)+2e^x$  \hspace{.5in} $f(x)=5\cos(x)-\tan(x)$  \hspace{.5in} $\displaystyle{f(\theta)=\frac{\cos(\theta)+7}{\sin(\theta)}}$

\vspace{2in}

\item For the limits below (if they exist).

$\displaystyle{\lim_{\theta\rightarrow 0}\frac{\sin(6\theta)}{2\theta}}$  \hspace{1in} $\displaystyle{\lim_{x\rightarrow 0}\frac{\sin(3x)\sin(5x)}{x^2}}$   \hspace{1in} $\displaystyle{\lim_{\theta\rightarrow 0}\frac{\cos(\theta)-1}{\sin(\theta)}}$ 

\vspace{2.5in}
\item Find an equation of the line tangent to $y=3x+6\cos(x)$ at the point $(\frac{\pi}{3}, \pi +3)$.

\end{enumerate}

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