# How do you differentiate f(x) = (x^3-3x^2+4)/x^2?

Apr 23, 2015

Well, you could use the quotient rule, if you know it, but the easier way (in my opinion) is to think first, differentiate second:

$f \left(x\right) = \frac{{x}^{3} - 3 {x}^{2} + 4}{x} ^ 2 = {x}^{3} / {x}^{2} - \frac{3 {x}^{2}}{x} ^ 2 + \frac{4}{x} ^ 2$, so

$f \left(x\right) = x - 3 + \frac{4}{x} ^ 2$.

$f \left(x\right) = x - 3 + 4 {x}^{- 2}$.

Therefore: $f ' \left(x\right) = 1 - 0 - 8 {x}^{- 3}$

$f ' \left(x\right) = 1 - \frac{8}{x} ^ 3$,

you may get a single denominator if you like.