Question

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

Answer 1

`f=x,g=x^2+1,f'=1,g'=2x->f'(x)=((gf'-fg')/g^2) =(x^2+1-2x^2)/(x^2+1)^2 = (1-x^2)/(x^2+1)^2`

Explanation:

Separate f and g and find their derivatives then plug in to the quotient rule and simplify