Question

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

Answer 1

I found: `f'(x)=cos(2x)/sin(2x)`

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 `2x`:

we get:

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

`=cos(2x)/sqrt(sin(2x))*1/sqrt(sin(2x))=cos(2x)/sin(2x)`