Question

U(x,y)=xy/(x+y), solve ∂U/∂x and ∂U/∂y

Answer 1

The trick to computing partial derivatives is to consider every other variable a constant.

Answer 2

yes, this I know, so tackle this as a standard quotient rule

Answer 3

Indeed, for the first one (the partial derivative with respect to x) just think of y as if its some arbitrary constant \(c\) and then compute the derivative as you normally would.

Answer 4

1/(x^2+2xy)

Answer 5

No not quite.

Answer 6

y^2/(x+y)^2

Answer 7

Yes, that's correct.

Answer 8

Now compute the partial derivative with respect to y.

Answer 9

x^2/(x+y)2

Answer 10

yep, looks like you're good to go.

Answer 11

thanks!