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 $f(x,y,z) = \frac{1}{\sqrt{x}}$, $g(x,y,z) = \sqrt{y}$, and $h(x,y,z) = \tan (x y)$
Answer:
$\left(
\begin{array}{ccc}
 -\frac{1}{2 x^{3/2}} & 0 & 0 \\
 0 & \frac{1}{2 \sqrt{y}} & 0 \\
 y \sec ^2(x y) & x \sec ^2(x y) & 0 \\
\end{array}
\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/calculus/jacobian/14626.txt'}