Question

F(x,y) = [(x^2+2y)^2 / (x^2 + y^2)]?
What is the partial derivative with respect to x?

Answer 1

So what you have is this:
F(x,y)= ((x^2+2y)^2) / (x^2+y^2)
Using the quotient rule when the equation has the form a/b:
(a´*b-a*b´) / (b^2)
So what we're doing is treating y as a constant since we are only interested in the partials with regards to x.
(4x(x^2+2y)(x^2+y^2) - ((2x)(x^2+2y)^2)) / ((x^2+y^2)^2)
Simplify from there on, are you with me on this?