What is the derivative of $ln (\sqrt{sin (2 x)})$ $ln(sqrt(sin(2x)))$ ?

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Answer 1 · 2016-03-19T00:59:45

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

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:

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

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

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