# How do you differentiate f(x)= ( x - 2)/ ( sin x ) using the quotient rule?

Apr 18, 2016

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

#### Explanation:

differentiate using the$\textcolor{b l u e}{\text{ quotient rule }}$

If f(x) $= \frac{g \left(x\right)}{h \left(x\right)} \text{ then } f ' \left(x\right) = \frac{h \left(x\right) . g ' \left(x\right) - g \left(x\right) . h ' \left(x\right)}{h \left(x\right)} ^ 2$
$\text{------------------------------------------------------------------------}$

g(x) = x - 2 $\Rightarrow g ' \left(x\right) = 1$

h(x) =$\sin x \Rightarrow h ' \left(x\right) = \cos x$
$\text{--------------------------------------------------------}$
substitute these values into f'(x)

$\Rightarrow f ' \left(x\right) = \frac{\sin x .1 - \left(x - 2\right) \cos x}{{\sin}^{2} x}$