Question

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

Answer 1

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

Explanation:

As `f(x)=x/(x^2+1)`, using quotient rule,

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

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

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