Problem:
Find the laplacian of the function $f(x,y,z)$ where $f(x,y,z) = \log \left(\frac{x}{y}+z^4\right)$
Answer:
$-\frac{x^2}{y^4 \left(\frac{x}{y}+z^4\right)^2}+\frac{2 x}{y^3 \left(\frac{x}{y}+z^4\right)}-\frac{1}{y^2 \left(\frac{x}{y}+z^4\right)^2}-\frac{16 z^6}{\left(\frac{x}{y}+z^4\right)^2}+\frac{12 z^2}{\frac{x}{y}+z^4}$
{'source': 'AMPS', 'file': 'amps/mathematica/calculus/laplacian/22063.txt'}