Let x, y and z be given parametrically by the arbitrary variables n & m:

x = ncos(m) + f'(m)sin(m);

y = nsin(m) - f'(m)cos(m);

z = n + f(m);

where f is a function of m, assumed to be derivable twice.

Then what are the partial derivates of z, with respect to the two variables x and y?