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So I have the function U(x,y). I have to find a partial derivative of U with respect to x. I understand that one can write that as U subscript x. But now I have to take d/dx of Ux, i.e. I have to take the derivative of Ux(x,y) with respect to x.

Supposedly the answer is Uxx + Uyx(dy/dx), but I don't really understand why...

Note that Ux = U subscript x

Note that Uyx = U subscript yx

Thank you in advance!