I have an odd question regarding partial differentiation. Suppose $f(x, y) = \int_1^{xy} e^{t^2}$. How would I go about finding $f_x, f_y$?
I know from other answers that applying the fundamental theorem of calculus for a different function works out much easier; suppose that instead $f(x, y) = \int_x^{y} e^{t^2}$. Then, we would let $G'(t) = e^{t^2}$, $f(x, y) = G(y) - G(x) $ which could be easily solved through partial differentiation. For my problem, the limits create mixed functions, which I'm not sure how to perform the partial derivative. Should I be applying the chain rule or some other information to find $G(xy)_x$?