Question

How do you find the derivative of `arcsin(sqrtsin13x)`?

Answer 1

Let's start with an uncommon method

`theta=arcsin(sqrtsin(13x))`
So
`sin(theta) = sqrt(sin(13x)`
derivate both side

`theta'cos(theta) = (13cos(13x))/(2sqrt(sin(13x))`

So we have

`theta'=(13cos(13x))/(2sqrt(sin(13x))*cos(theta)`

Buuuuuut : `cos(theta) = sqrt(1-sin^2(theta)`

and `sin^2(theta) =sin(13x)`

So...

`theta'=(13cos(13x))/(2sqrt(sin(13x))*sqrt(1-sin(13x))`

You can check with wolfram alpha !