Question

How do you differentiate `(4x − 2) / (x^2 + 1)`?

Answer 1

`d/(dx)((4x-2)/(x^2+1))=(-4x^2+4x+4)/(x^2+1)^2`

Explanation:

To differentiate this, use the quotient rule:

`(f/g)^'=(f^'g-fg^')/g^2`

In this case, `f=4x-2` and `g=x^2+1`. It then follows that `f^'=4` and `g^'=2x`. Plugging all of these expressions into the formula gives

`(4(x^2+1)-(4x-2)(2x))/(x^2+1)^2=(-4x^2+4x+4)/(x^2+1)^2`