Question

How do you use the Quotient Rule to differentiate the function `f(x)=(x)/(x^2+1)`?

Answer 1

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

Explanation:

The Quotient Rule tells you that if you have a function such as: `f(x)=g(x)/(h(x))` the derivative will be:
`f'(x)=(g'(x)h(x)-g(x)h'(x))/[h(x)]^2` where `'` indicates derivative.
In your case you get:
`f'(x)=(1(x^2+1)-x(2x))/(x^2+1)^2=(x^2+1-2x^2)/(x^2+1)^2=(1-x^2)/(x^2+1)^2`