I found it to be: 3,486,784,401sin(3x), by using the chain rule, but my homework says that it is wrong. Since the derivative of cosx is -sinx and the derivative of sinx is cosx I just alternated between sin and cos and changed the sign of the expression every other time until I got to the 20th derivative. I also just took 3^20 and used that as the constant out in front.
-
3^20 sin(3x) = 3,486,784,401sin(3x) is correct. What's the answer did your teacher give?