How to find the partial derivative of $f(x, y) = x^{2} - y^{2}$ with respect to $y.$ Recently, I began exploring the realms of multi-variable calculus, and, already, I have ran into a problem.
I am trying to find the partial derivative of $f(x, y) = x^{2} - y^{2}$ with respect to $y$.
I believe it to be $-2y,$ but I am not sure, as Wolfram Alpha seems to be giving me this rather daunting result.

You are correct, since if you derivate with respect to $y$, $x^2$ will count only as a constant, and the derivate of any constant is $0$. Since derivating is additive, you can do it by first derivating $x^2$, and then derivating $y^2$. The first will  be $0$, the second is $2y$, therefore your answer is $0-2y=-2y$. Totally correct. :)
