Derivatives suck~!...Help please!?

Question

Can anyone help me find this one...I get realy confused these....

I need to find the deriviative in respect to x and y
F (x,y) = x^2 + y^2/x^2-y^2

Answer 1

For the partial derivatives with respect to x and y, use the quotient rule.

dF/dx = [(x^2-y^2)(2x) - (x^2+y^2)(2x)] / (x^2-y^2)^2
= -4xy^2 / (x^2-y^2)^2.

dF/dy = [(x^2-y^2)(2y) - (x^2+y^2)(2y)] / (x^2-y^2)^2
= -4y^3 / (x^2-y^2)^2.

Answer 2

if u mean (x^2+y^2)/(x^2-y^2) rewrite as (x^2+y^2)*(x^2-y^2)^-1 and use product rule d(uv)=u*dv+v*du with u = x^2+y^2 and v = (x^2-y^2)^-1

for Dx[u]=2x Dx[v]= -1(X^2-y^2)^-2*2x=-2x/(x^2-y^2)^2

udv+vdu=(x^2+y^2)*(-2x)/(x^2-y^2)^2+(x^2-y^2)^-1*2x


repeat this process finding Dy[u] and Dy[v] and piece together udv+vdu

by the way derivatives dont suck they provide a way to determine rate of change in a quantity when amount of change in said quantity is known this is very useful!!!!

Answer 3

Wow, I wish I could help but I just started with derivatives and this doesn't look fun. Guess this is what I have to look forward to. Great. Well good luck!