Question

How do you differentiate `f(x) = (x^2-4x)/(x+1)` using the quotient rule?

Answer 1

`f'(x) = ((2x - 4)(x+1) - x^2 + 4x)/(x+1)^2`

Explanation:

Let `f(x) = (u(x))/(v(x))` where `u(x) = x^2 - 4x` and `v(x) = x+1`.

By the quotient rule, `f'(x) = (u'(x)v(x) - u(x)v'(x))/(v(x))^2`. Here, `u'(x) = 2x - 4` and `v'(x) = 1`.

So `f'(x) = ((2x - 4)(x+1) - x^2 + 4x)/(x+1)^2` by direct use of the quotient rule.