Question

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

Answer 1

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

Explanation:

Using the Quotient Rule,

`f'(x)=((1+x^2)d/dx(x)-xd/dx(1+x^2))/(1+x^2)^2`

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

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

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

This is as much simplification as we can do.