Question

How do you use the quotient rule to differentiate `f(x)=(x)/(x2+1)`?

Answer 1

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

Explanation:

We have: `f(x) = (x) / (x^(2) + 1)`

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

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

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