# How do you find the derivative of (x)=(x)/(x^2+1)?

$f = x , g = {x}^{2} + 1 , f ' = 1 , g ' = 2 x \to f ' \left(x\right) = \left(\frac{g f ' - f g '}{g} ^ 2\right) = \frac{{x}^{2} + 1 - 2 {x}^{2}}{{x}^{2} + 1} ^ 2 = \frac{1 - {x}^{2}}{{x}^{2} + 1} ^ 2$