Hi all,

I have differentiated $\displaystyle y = \frac{e^{4x}sinx}{xcos2x}$, using the quotient rule to get:

$\displaystyle \frac{dy}{dx}=\frac{xcos2x.e^{4x}(4sinx+cosx)-e^{4x}sinx(cos2x-2xsin2x)}{(xcos2x)^2}$

how can I simplify this further? please can you show step by step as I always make silly mistakes when trying to simplifly.

this is what the teacher said it is in simplest form:

$\displaystyle \frac{e^{4x}sinx(4+cotx-x^{-1}+2tan2x)}{xcos2x}$

thanks