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?