anonymous
  • anonymous
partial derivative f(x,y) = [(xy)^(1/2)] e^y with respect to x and y????
Mathematics
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anonymous
  • anonymous
partial derivative f(x,y) = [(xy)^(1/2)] e^y with respect to x and y????
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Partial derivative you just treat the other variable as if it were a constant.
anonymous
  • anonymous
so with the first partial derivative with respect to y, you will use the chain rule and product rule, and view x as a constant so \[f _{y}=xe^y/(2\sqrt{xy}) +\sqrt{xy}e^y\] for x\[f_{x}=ye^y/(2\sqrt{xy})\], to make it clearer, you can use the product rule again, but the e^y would just be a derivative of a constant and the sum is added to zero.
anonymous
  • anonymous
it is like pj said, you view whicher variable you are not differentiating as a constant.

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anonymous
  • anonymous
how did you get the second part in Fy?
anonymous
  • anonymous
xy^(1/2)*d/dy e^y = xy^(1/2)e^y. remember e^y or x will = the same as a derivative. The second part of the product rule would be f(y)*g'(y)

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