Question

partial derivative f(x,y) = [(xy)^(1/2)] e^y with respect to x and y????

Answer 1

Partial derivative you just treat the other variable as if it were a constant.

Answer 2

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.

Answer 3

it is like pj said, you view whicher variable you are not differentiating as a constant.

Answer 4

how did you get the second part in Fy?

Answer 5

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)