# How do you use the Quotient Rule to differentiate the function f(x)=(x)/(x^2+1)?

I found: $f ' \left(x\right) = \frac{1 - {x}^{2}}{{x}^{2} + 1} ^ 2$
The Quotient Rule tells you that if you have a function such as: $f \left(x\right) = g \frac{x}{h \left(x\right)}$ the derivative will be:
$f ' \left(x\right) = \frac{g ' \left(x\right) h \left(x\right) - g \left(x\right) h ' \left(x\right)}{h \left(x\right)} ^ 2$ where $'$ indicates derivative.
$f ' \left(x\right) = \frac{1 \left({x}^{2} + 1\right) - x \left(2 x\right)}{{x}^{2} + 1} ^ 2 = \frac{{x}^{2} + 1 - 2 {x}^{2}}{{x}^{2} + 1} ^ 2 = \frac{1 - {x}^{2}}{{x}^{2} + 1} ^ 2$