# What is the derivative of ln(sqrt(sin(2x)))?

Mar 19, 2016

I found: $f ' \left(x\right) = \cos \frac{2 x}{\sin} \left(2 x\right)$

#### Explanation:

This is quite good!

We can recognize 4 functions nested one into the other!!!

We can use the Chain Rule deriving (from the outher to the inner):
$\ln$ then $\sqrt{}$ then $\sin$ and finally $2 x$:

we get:

f´(x)=1/sqrt(sin(2x))1/(2sqrt(sin(2x)))cos(2x)*2=

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