Question

How do you differentiate `f(x)=(x+1)/(x-1)` using the quotient rule?

Answer 1

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

Explanation:

`f(x) = (x + 1)/(x - 1)`

Let say,
`u = x + 1, u' = 1`, and
`v = x - 1, v' = 1`

`f(x) = u/v`, then
`f'(x) = (u'v - uv')/v^2`

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

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

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