i'm having trouble a bit of trouble with taking the derivatives and collating my results of trig functions in the form of $sin$ $3x$ for example.
The specific problem i'm stuck on is;
Find the derivative of $2\sin3t\cos4t$
I'll show what I have done, but i'm really looking for some explanation of a general case for this type of problem.
I let $u$ $=$ $2\sin3t$ and $v=\cos4t$
$dv/dt = -4\sin4t$
$d/dt[2\sin3t\cos4t] = u\cdot dv/dt +v\cdot du/dt$
Firstly, are there any glaring mistakes in the above?
and secondly, my book says the answer should be $7\cos(7t) - \cos(t)$. I'm unsure of how to simplify my answer down to actually check it against the book.
I'd appreciate some general help on how I treat functions in this format.