Question

What is the derivative of `y=(x^2 - 1) /( x+1)`?

Answer 1

`2/(x^2-1)`

Explanation:

Use the quotient rule, which states that if `f(x) = g(x)/(h(x))` then
`f'(x) = (h(x)g'(x) - h'(x)g(x))/(g^2(x))`

`g(x) = (x^2-1)` so `g'(x) = 2x`
`h(x) = (x+1)` so `h'(x) = 1`

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