## Commpute Laplace's equation Uxx+Uyy+Uzz=0 given set of spherical coordinates

Hello,

We were given the question below as hw but I am having major issues. I have tried this for over an hour. Please help!

Spherical coordinates (p, theta, phi) are defined by
x=pcos(theta)sin(phi)
y=psin(theta)sin(phi)
z=pcos(theta)

Compute Laplace's equation uxx + uyy + uzz = 0 in spherical coordinates.

I have already tried for example computing d/dp=du/dx*dx/dp + du/dy*dy/dp + du/dz*dz/dp
and the same for d/d(theta) and d/d(phi)...

Then I put them into matricies and used Cramer's rule to solve for du/dx which is as far as I have gone so far. Is this correct because my du/dx does not look very clean and there is a ton of computation and I don't even know how to find Uxx, Uyy, Uzz after this... I would really appreciate some help.