Find the surface ara of the sphere that lies inside the paraboloid , using cylindrical co-ords.

What I've done:

equations of the sphere and paraboloid in cylindrical co-ordinates are and .

substituting and rearranging these gives

this gives the points of intersections

And that's as far as I can get. I'm having a problem with the partial derivatives.

To get them I've done this:

When I differentiate, am I right in assuming the 'z' on the RHS disappears as well? Does it go to 1 or 0?

ie.

or: