Question

How do you differentiate `f(x)=(x^2-2x)/(x+3)^2` using the quotient rule?

Answer 1

`f'(x) = ((2x-2)(x+3)^2 - 2(x^2 - 2x)(x+3))/(x+3)^4 = (df)/dx`

Explanation:

You know that the derivative of the quotient of two functions `u` and `v`is given by the formula `(u'v - uv')/v^2`.

Here, `u(x) = x^2 - 2x` and `v(x) = (x+3)^2` so `u'(x) = 2x-2` and `v'(x) = 2(x+3)` by the power rule. Hence the result.