Question

What is the derivative of `x^2/(x^2 +3)`?

Answer 1

`d/(dx) (x^2/(x^2+3))=(6x)/(x^2+3)^2`

Explanation:

Using a combination of the chain rule and power rule, we have:

`d/(dx) (u(x))^n = n(u(x))^(n-1)u'(x)`

Hence:

`d/(dx) (x^2/(x^2+3))=d/(dx) (((x^2+3)-3)/(x^2+3))`

`color(white)(00)=d/(dx) (1-3(x^2+3)^(-1))`

`color(white)(00)= 0-3(-1)(x^2+3)^(-2)(2x)`

`color(white)(00)=(6x)/(x^2+3)^2`