Partial derivative of what?x = rcos(t) and y = rsin(t), find dr/dx and dr/dy(partial derivatives)...........I get all that, but if we go back to x = rcos(t) and y = rsin(t), couldn't we just rearrange these to make r the subject, the take the partial derivatives of that? But this gets (dr/dx) = 1/cos(t) and (dr/dy) = 1/sin(t), so it obviously can't be right, but where is it incorrect? I'm probably missing something simple...

If you meant to take the derivative with respect to and of the function composed of and Then:

Then do implicit differentiation of with respect to which is:

And then with respect to :

Or if you meant of and of , then the answer and is correct.

Two different answers based on which function you choose to differentiate.