Problem:
Find the jacobian of the vector valued function $\begin{pmatrix} f(x,y,z)\\ g(x,y,z) \\ h(x,y,z)\end{pmatrix}$ where $f(x,y,z) = \frac{1}{x^2}$, $g(x,y,z) = \log (x)$, and $h(x,y,z) = \tan ^{-1}(z)$
Answer:
$\left(
\begin{array}{ccc}
 -\frac{2}{x^3} & 0 & 0 \\
 \frac{1}{x} & 0 & 0 \\
 0 & 0 & \frac{1}{z^2+1} \\
\end{array}
\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/calculus/jacobian/2899.txt'}