# How do you differentiate f(x) = x^3/sinx using the quotient rule?

Jan 14, 2016

$\frac{{x}^{2} \left(3 \sin x - x \cos x\right)}{\sin} ^ 2 x$

#### Explanation:

The quotient rule states that:

$\frac{d}{\mathrm{dx}} \left(\frac{u}{v}\right) = \frac{v u ' - u v '}{v} ^ 2$

$u = {x}^{3} , v = \sin x$
$u ' = 3 {x}^{2} , v ' = \cos x$

$\frac{d}{\mathrm{dx}} \left({x}^{3} / \sin x\right) = \frac{\sin x \cdot 3 {x}^{2} - {x}^{3} \cdot \cos x}{\sin} ^ 2 x$

$= \frac{{x}^{2} \left(3 \sin x - x \cos x\right)}{\sin} ^ 2 x$