Question

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

Answer 1

`(-10x)/(x^2+1)^2`

Explanation:

Let `u=5` and `v=x^2+1`

`u' = 0 and v'=2x`

Let say `y=5/(x^2+1) =u/v`

`y'=(vu'-uv')/v^2`

`y'=((x^2+1)*0-5(2x))/(x^2+1)^2`

`y'=(-5(2x))/(x^2+1)^2`

`y'=(-10x)/(x^2+1)^2`