Take the function
$f(x) = \sin(2x) \cdot \cos(x)$
Find the 2013 th derivative
What I have found so far:
$f''(x)= -4\sin(x) \cdot \cos(2x) - 5f(x)$
I am assuming I need to find a relationship such as the above in order to just apply it again and again, however I can't seem to do so.
Any help is appreciated. Thank You.
EDIT: @Ihsan and Babak
Utilising this result, results in:
$f''(x) = -8\sin(3x) - f(x) $
And I'm not sure how to make recur this 1006 times!