Question

How do you differentiate `y = x / (x^2 + 3 )`?

Answer 1

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

Explanation:

Use the formula for derivatives of quotients

`d/dx(u/v)=(v (du)/dx-u (dv)/dx)/v^2`

Let `u=x`
Let `v=x^2+3`

`dy/dx=((x^2+3)*1-x(2x))/(x^2+3)^2`

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