Many of your are asking about this problem. Make sure to simplify your function before taking the derivatives. I mean, really, you could take the derivative of

\[f(x,y)=\cos(x)-\cos(x)+\sin(y)-\sin(y)\]

by differentiating the trig functions, but that would be silly. If you want more of a hint, recall that

\[u^2\cos^2(v)+u^2\sin^2(v)=u^2.\]

So yes, for many of you (depending on the randomness of the functions given to you), the derivative with respect to one of the variables is actually a number.

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