# How do you find the derivative of y= 1 / (2 sin 2x)?

Apr 13, 2018

The derivative is $= - \frac{\cos 2 x}{{\sin}^{2} 2 x}$

#### Explanation:

We need

$\left(\frac{1}{u \left(x\right)}\right) ' = - \frac{u ' \left(x\right)}{u \left(x\right)} ^ 2$

Here,

$y = \frac{1}{2 \sin \left(2 x\right)}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2} \cdot \left(\frac{1}{\sin} \left(2 x\right)\right) '$

$= \frac{1}{2} \cdot \left(- \frac{1}{{\sin}^{2} 2 x}\right) \cdot 2 \cos 2 x$

$= - \frac{\cos 2 x}{{\sin}^{2} 2 x}$