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 $f(x,y,z) = e^{x^3}$, $g(x,y,z) = \sqrt[3]{y^3}$, and $h(x,y,z) = \frac{1}{\sqrt{z}}$
Answer:
$\left(
\begin{array}{ccc}
 3 e^{x^3} x^2 & 0 & 0 \\
 0 & \frac{y^2}{\sqrt[3]{y^3}^2} & 0 \\
 0 & 0 & -\frac{1}{2 z^{3/2}} \\
\end{array}
\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/calculus/jacobian/47004.txt'}