Please see the attached document regarding homework specifics.
Thank-you for your help.
I have attached both versions of Microsoft Word (just in case).
Let f: ℝ3 → ℝ be differentiable. Making the substitution
x = ρ cos(θ) sin(φ), y = ρ sin(θ) sin(φ), z = ρ cos(φ)
(spherical coordinates) into f:(x,y,z), compute
Please find the solution in the attached ...
This provides an example of working with differentiable functions and substitutions.