Question

How do you differentiate `f(x)= x/(x+1)`?

Answer 1

You can use the Quotient Rule where you have:
`f(x)=g(x)/(h(x))`
`f'(x)=[g'(x)h(x)-g(x)h'(x)]/[h(x)]^2`
in your case you get:
`f'(x)=[1(x+1)-x*1]/(x+1)^2=1/(x+1)^2`

Answer 2

Use the quotient rule:

`(T/B)'=(T'B-TB')/B^2`

In this problem`f(x)=x/(x+1)`

`T=x`, so `T'=1`

`B=x+1`, so `B'=1`

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