Please check my derivative if its correct

[HelloMotto]

Homework Statement

find a formula for the derivative of the function y = f(x) that satisfies the equation below.

Homework Equations

$$\frac{1}{x^{2}+y^{2}}\$$ = 2xy

The Attempt at a Solution

so my final answer is

2x⁴f(x)+4x²f(x)²+2f(x)³
all over
-2f(x)-2x⁵-4x³f(x)-2xf(x)²

Am i doing it right? I have a feeling I may have misunderstood the question.

 

[seto6]

so if you differetiate y=f(x) you should get what's below?

LaTeX Code: \\frac{1}{x^{2}+y^{2}}\\ = 2xy


well you can integrate wrt x since function is interms of x. then you can get the original function