SOLUTION: given: u = √(xy) solve: [(du/dx)/(du/dy)]

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Question 404115: given: u = √(xy)
solve: [(du/dx)/(du/dy)]
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not too familiar with multi-variable calculus, but I'll try my best...

We have:

du%2Fdx+=+%281%2F2%29%281%2Fsqrt%28xy%29%29%28y%29, applying the chain rule. Here, y is treated as a constant.

du%2Fdy+=+%281%2F2%29%281%2Fsqrt%28xy%29%29%28x%29 by the same logic. Therefore, %28du%2Fdx%29%2F%28du%2Fdy%29+=+y%2Fx.