%% Math 131, Fall, 2003
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\newcommand{\ddx}[1]{\ds\frac{d}{d#1}}

\begin{document}

\begin{center}
\textbf{Holy Cross College, Fall Semester, 2003} \\
\textbf{Math 131, Professor Hwang} \\
Worksheet for Thursday, October~23
\end{center}

Compute the indicated derivatives:

\be

\item $\ddx{x}xe^{-x}$,\qquad $\ddx{x} x^2e^{-x}$,\qquad $\ddx{x} x^ne^{-x}$
\vfil

\item $\ddx{u}\frac{e^u}{u^2+5}$,\qquad $\ddx{t}\frac{e^u}{u^2+5}$
  (assume~$u$ is a function of~$t$)
\vfil

\item $\ddx{w}\frac{\cos w}{w^2+5}$,\qquad $\ddx{v}\frac{v^2+5}{\sin v}$
\vfil

\item $\ddx{x}\ln(x^2)$,\qquad $\ddx{x}\ln x^5$,\qquad $\ddx{x}(x^n)$
  (Is this result surprising?)
\vfil

\item $\ddx{s}\ln(s^2+1)$,\qquad $\ddx{x}\ln(\cos x)$
\vfil

\ee
\eject

\end{document}
