Thread: involved derivative

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?

Originally Posted by tombrownington

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?

Maybe someone more knowedgable will come and answer this, but I have a question of clarification. You do not have explicitly as a function of . Is that intentional? Are we supposed to solve for ?

yup. that's the way it is. z is given in function of u and v, not x and y.
solving for u and v is impracticable since the function f(m) is introduced in z while its derivative is given in x and y.

Can one at least write: