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 $f(x,y,z) = x^{3/2}$, $g(x,y,z) = \sin (y z)$, and $h(x,y,z) = (z-x)^{3/2}$
Answer:
$\left(
\begin{array}{ccc}
 \frac{3 \sqrt{x}}{2} & 0 & 0 \\
 0 & z \cos (y z) & y \cos (y z) \\
 -\frac{3 \sqrt{z-x}}{2} & 0 & \frac{3 \sqrt{z-x}}{2} \\
\end{array}
\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/calculus/jacobian/12236.txt'}