Spherical to rectangular within a function?

Question

Show that fxx + fyy + fzz = 0 when w= f(r,theta,z) = ln(r) +3z

I thought I could just take the second derivs based on r,theta,z, but that doesnt work out. So im guessing I need to convert into x,y,z, but I can't figure out how to do that.

Help is appreciated. Always give best answer.

Answer 1

Is that really spherical? It looks more cylindrical.

E.g., I'd think x = rcos(theta), y = r sin(theta), and z just is z.

And so r = (x^2 + y^2)^.5

And what you're supposed to prove doesn't look true at all.

I recommend you recheck for misreadings/typos.