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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 3}\quad {\sl Feb. 9, 1995}

\begin{enumerate}
\problemspace
\item Compute the derivative of $f(x) = (1+x^2)^{\sqrt{1+x^2}}$.
\answerspace

\problemspace
\item 
  \begin{enumerate}[a)]
  \item Define the hyperbolic trig functions, $\cosh(x)$,
  $\sinh(x)$, and $\tanh(x)$.
  \answerspace
  \item Derive the derivatives of $\cosh(x)$, $\sinh(x)$, and $\tanh(x)$.
  \answerspace
  \item Derive a formula for $\sinh^{-1}(x)$, the inverse function of
  $\sinh(x)$; state its domain and range.
  \answerspace \end{enumerate}

\problemspace
\item 
  \begin{enumerate}[a)]
  \item State and prove the Theorem on Derivatives of Inverse Functions.
  \answerspace
  \item Prove that ${d\over dx}\arcsin(x) = {1\over\sqrt{1-x^2}}$.
  \answerspace
  \end{enumerate}

\problemspace
\item \textsc{Bonus Question:} Derive a formula for the
derivative of the infinite exponential function
$y = x^{x^{x^{\dots}}}$, defined for
$0<x \le e^{1/e}$ as the inverse of $x = y^{1/y}$.
\end{enumerate}

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