# How do I use the quotient rule to find the derivative?

Oct 5, 2014

Quotient Rule

$\left[\frac{f \left(x\right)}{g \left(x\right)}\right] ' = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{{\left[g \left(x\right)\right]}^{2}}$

Let us look at the following example.

$\left(\frac{x}{{x}^{2} + 1}\right) '$

by Quotient Rule above,

$= \frac{1 \cdot \left({x}^{2} + 1\right) - x \cdot 2 x}{{\left({x}^{2} + 1\right)}^{2}}$

by cleaning it up a bit,

$= \frac{1 - {x}^{2}}{{\left({x}^{2} + 1\right)}^{2}}$

I hope that this was helpful.