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{\bf Quiz \#7; Tuesday, date: 03/06/2018}
{\bf MATH 53 Multivariable Calculus with Stankova}
{\bf Section \#117; time: 5 -- 6:30 pm}
{\bf GSI name: Kenneth Hung}
{\bf Student name:}
\vspace*{0.25in}
\begin{enumerate}
\item Find the first partial derivatives of $f(x, y) = x^y$. Then use chain rule to find the derivative of $t^t$ with respect to $t$.
\item {\em True / False?} Given a function at $f$, defined on a disc near the origin. To show that $f$ is not differentiable at the origin, it suffices to find three curves through the origin, such that their tangent lines at the origin do not lie on the same plane.
\item {\em True / False?} Suppose
\[
z = f(x, y), ~~~~ x = g(t, u), ~~~~ y = h(u, v),
\]
then by chain rule we have
\[
\frac{\partial z}{\partial t} = \frac{\partial z}{\partial x} \frac{\partial x}{\partial t}.
\]
\end{enumerate}
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