# What is the derivative of 5/(x^2+1)?

Jan 23, 2017

$\frac{- 10 x}{{x}^{2} + 1} ^ 2$

#### Explanation:

Let $u = 5$ and $v = {x}^{2} + 1$

$u ' = 0 \mathmr{and} v ' = 2 x$

Let say $y = \frac{5}{{x}^{2} + 1} = \frac{u}{v}$

$y ' = \frac{v u ' - u v '}{v} ^ 2$

$y ' = \frac{\left({x}^{2} + 1\right) \cdot 0 - 5 \left(2 x\right)}{{x}^{2} + 1} ^ 2$

$y ' = \frac{- 5 \left(2 x\right)}{{x}^{2} + 1} ^ 2$

$y ' = \frac{- 10 x}{{x}^{2} + 1} ^ 2$