Please check my derivative if its correct

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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.
 
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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
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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