How do you differentiate (1/3)cos12x-(1/4)sin12x?

Question

i tried and i got -4sin12x-3cos12x, but i dont think its right. after you get the differentiation, could you set it to 0 and solve for x? and show the steps? i completely forgot how to do trig but i think this will help. thanks!

Answer 1

The usual way. Let 12 x = u, and du/dx=12
Then we have f(u)= 1/3 sin u - 1/4 cos u. taking df(u)/du, -4 cos u + 3 sin u. Back substituting u=12x, you get your answer. Of course you can set this to 0 to get a mininum or maximum. Doing this, 4 cos u = 3 sin u , and tan u = 4/3. Then
arctan (4/3) = u = 12x. Since the original function is periodic, the min or max will occur periodically.