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

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Answer 1 · 2016-01-17T18:57:53

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

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.

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