Question

How do you calculator the derivative for `(2x-5)/(x^(2)-4)`?

Answer 1

The quotient rule says that for some `h(x) = f(x)/(g(x))`, the derivative is:

`h'(x) = [g(x)f'(x) - f(x)g'(x)]/(g(x))^2`

so we get:

`h'(x) = [(x^2-4)(2) - (2x-5)(2x)]/(x^2-4)^2 = (2x^2- 8 - 4x^2 + 10x)/(x^2-4)^2`
`= (-2x^2+10x-8)/(x^2-4)^2`
`= [(-2x + 2)(x - 4)]/(x^2-4)^2 = [2(-x+1)(x - 4)]/(x^2-4)^2`