Question

How do you find the derivative of `(X/(X^2+1))`?

Answer 1

Using quotient rule, which states that for `y=f(x)/g(x)`,

`y'=(f'(x)g(x)-f(x)g'(x))/(g(x))^2`,

We can proceed to derivate this with no big problems.

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

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

`color(green)((dy)/(dx)=(-x^2+1)/(x^2+1)^2)`