Gradient and Divergence in spherical coordinates

[physicss]

Homework Statement

Hello, are my answers correct?

I had to calculate the gradient of f=z and f=xy in spherical coordinates.
My solution for f= z is: cos(θ) er+ (-sin(θ)) e(θ)

f=xy

rsin^2(θ)sin(2φ) er+ rcos(θ)cos(φ)sin(θ)sin(φ) e(θ)+ rcos(2φ)sin(θ) e(φ)

I also had to calculate the divergence of the following vectorfield (Image)

My result is: (scalarfield)

Sin^2(θ)cos^2(φ) er + rcos(2θ)cos^2(φ) e(θ)-rsin(θ)cos(2φ) e(φ)


Thanks in advance

Relevant Equations

er, e(θ) and e(φ) are the spherical base vectors

Vectorfield for the divergence

 

[haruspex]

rsin^2(θ)sin(2φ) er+ rcos(θ)cos(φ)sin(θ)sin(φ) e(θ)+ rcos(2φ)sin(θ) e(φ)

I get a slightly different ##\vec e_\theta##.
Please learn to use LaTeX.

 

[haruspex]

My result is: (scalarfield)

Sin^2(θ)cos^2(φ) er + rcos(2θ)cos^2(φ) e(θ)-rsin(θ)cos(2φ) e(φ)

If it is a scalar, how come it has ##\vec e_r## etc?
I also note a dimensional inconsistency.