I am wondering because I have tried to answer this question, but have gotten a different answer: $(4-6x)\sin(2x)+(4x+6)\cos(2x)$.
To get the above answer I did the following steps:
1) Product rule: $ \quad x[-6\sin(2x)+4\cos(2x)]+1[6\cos(2x)+4\sin(2x)]$
2) Group like terms: $\quad [-6x\sin(2x)+4\sin(2x)]+[4x\cos(2x)+6\cos(2x)]$
3) Factor out $\cos(2x)$ and $\sin(2x)$: $\quad (4-6x)\sin(2x)+(4x+6)\cos(2x)$
Does anyone know where I went wrong?
If so, can you please explain what I should have done to get the right answer?
All help is appreciated.