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\begin{document}
\begin{center}

\Huge{Explicit Differentiation Practice}
\end{center}
\normalsize
\noindent


For each of the functions below find their respective derivatives.

\begin{enumerate}
\item Review: $\sqrt{x^3-5}$ \hspace{1.5in} $(x^3-1)^{100}$\hspace{1.5in}$e^{3x^2-x}$\\
\vfill


\item Notice that we can use the product, quotient, and chain rule together in the same problem.  The trick is to use the notation to \emph{guide} you.  Find the derivative of the following functions:

$\sin^5(x)\sqrt{x^3-5}$
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\item The chain rule can also be used in conjunction with itself.  That is, we can use the chain rule to work on a derivative, but when trying to find the ``inside function", we may need to use the chain rule \emph{again}.  


%$\sqrt {47+3e^{3x^2-x}}$\\
%\vfill
$\sin^2(x^3)$
\vfill

\end{enumerate}


\newpage

\begin{center}
\Huge{Implicit Differentiation Practice}
\end{center}
\normalsize
\noindent

\vspace{-.2in}
\begin{enumerate}
\item Assume that $y$ is a function of $x$. Find $\frac{dy}{dx}$ in the following:
\begin{enumerate}
\item $x^3+y^3=8$
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\item $y=x^2y^3+x^3y^2$
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\item $y=\sin (2x+5y)$
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\item $e^{xy}=e^{3x}-e^{4y}$
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\end{enumerate}

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