Very hard derivative w/ 'e' and trig function! Please help!?

Question

Find the derivate of:
q=[e^(-0.1t)](0.2sin120πt+0.8cos120πt)

I know these type of problems are hard to visualize with it all typed in one straight line, so to clarify:

(-0.1t) is the exponent for 'e', and everything else is multiplied by the result of e^(-0.1t)
Any help would be greatly appreciated.

It looks like part of the problem got cut off. The second set of parenthisis is:
0.2sin120πt+0.8cos120πt

Answer 1

Just already correctly answered: why repost

q=[e^(-0.1t)] (0.2sin120πt+0.8cos120πt)

let 120 pi=k

q=[e^(-0.1t)] (0.2sin kt+0.8cos kt)

dq/dt = [e^(-0.1t)] [ 0.2 k cos kt - 0.8 k sin kt)] -
............. - 0.1 e^(-0.1t)] [0.2sin kt+0.8cos kt]

dq/dt = e^(-0.1t) { sin kt * [- 0.02 - 0.8k] + cos kt*[0.2 k - 0.08]}

dq/dt = e^(-0.1t) {- sin kt * [0.8k+ 0.02] + cos kt [0.2 k - 0.08]}

**** 120 pi=k so 0.8 k = 96 pi and 0.2k= 24 pi

dq/dt = e^(-0.1t) {-[96 Pi+ 0.02] sin kt + [24 pi-0.08] cos kt}