Question 404115
I'm not too familiar with multi-variable calculus, but I'll try my best...


We have:


{{{du/dx = (1/2)(1/sqrt(xy))(y)}}}, applying the chain rule. Here, y is treated as a constant.


{{{du/dy = (1/2)(1/sqrt(xy))(x)}}} by the same logic. Therefore, {{{(du/dx)/(du/dy) = y/x}}}.