Mean curvature of a surface

Hi everyone, new here and trying to calculate the mean curvature for the following surface:

r(u,v)=ui+f(u)cos(v)j+f(u)sin(v)k


I have been through the process of finding tangent vectors and a unit normal vector to the surface, so up to the point where I have had to substitute 6 scalars into:

h(p)=
aG-2bF-cE
2(EG-F²)

The only problem I seem to be having is not being able to simplify it... This is what I have:

h(p)=
± f''(u)f(u)²-f'(u)²-1
2f(u)(1+f'(u)²)√(cos²(2v)f'(u)+1)

Maybe missing something really simple here or I have made a mistake in calculating the scalars.

Any help, much appreciated!

Attachment 27245

I have worked through this again and shamefully the original post had some errors in. I have attached a correct answer, however still stuck with having to derive the differential equation!

From this link, because it would be a lot of typesetting:

Attachment 27465

Replace S(x,y) with your r(u,v). Respond with calculated partial derivatives as in the formula so we can see where you are going wrong.