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\noindent
{\bf Math 1030 Workshop \#4} \hfill
{\bf Name: \underline{\hspace*{2.5in}}}

\vspace{0.05in}

\noindent
{\Large \bf DUE: Friday, July 22${}^{\mbox{nd}}$} Please turn in a paper copy and
{\bf SHOW YOUR WORK!}

\vspace{0.05in}

\begin{enumerate}
   \item Use the limit definition of the derivative to find $f'(x)$ if...\\
         {}[You use should the rules we learned to double check your answer.]

   \begin{enumerate}
      \item $f(x) = -4x^2+2x-1$

\vspace{2.1in}

      \item $f(x) = \dfrac{1}{\sqrt{x}}$ 

\vspace{2.1in}

   \end{enumerate}

   \item Find the equation of the line tangent to the graph of $y = f(x)$ at $x=x_0$
         if...

   \begin{enumerate}
      \item $f(x) = x^3-x^2+x-1$ and $x_0=-2$

\vspace{1.5in}

      \item $f(x) = \ln(x)$ and $x_0=1$

\vspace{1.5in}

   \end{enumerate}

   \item Compute the derivative of each of the following functions. 

   \begin{enumerate}
      \item $y = 8\sqrt[4]{x}-7\ln(x)+2e^x-\dfrac{9}{x^{5}}+3x+\sqrt{57}$  % standard stuff

\vspace{1.7in}

      \item $y = x^7\ln(x+1)$  % product rule

\vspace{1.7in}

      \item $\displaystyle{y = \frac{x^2e^x+5x-1}{x^3+4}}$  % quotient rule

\vspace{1.7in}

      \item $\displaystyle y = \Big(e^{x^3}+11x-6\Big)^{45}$  % double chain rule

\vspace{1.7in}

      \item $\displaystyle{y = \ln\left(\frac{11\sqrt[3]{x}\,e^{-8x}}{(x^2+1)^6(x-2)^{100}}\right)}$ % log problem

\vspace{1.7in}

   \end{enumerate}

\end{enumerate}

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