Compute the derivative of the function
![\[ f(x) = \cos (2x) - 2 \sin x. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-97cc431aca9e5f8a18ae90fe0bd2462f_l3.png "Rendered by QuickLaTeX.com")
Using the chain rule we compute,
![\[ f'(x) = -2 \sin (2x) - 2 \cos x = -2 \cos x (1 + 2 \sin x), \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-e622030a26e959971a8a5f4dd1c6cd9c_l3.png "Rendered by QuickLaTeX.com")
where we used the trig identity 
in the second step.
Compute the derivative of the function
Using the chain rule we compute,
where we used the trig identity in the second step.