Find the nth derivative of (sin x)^3

You'll need to try to find the pattern that applies here.  Find the 1st, 2nd, 3rd, 4th and 5th derivatives.  Is a pattern evident?

n=1:  first derivative of (sin x)^3 is 3(sin x)^2*cos x (which is a product)

n=2:  second deriv. of (sin x)^3 is 3(sin x)^2*(-sin x) + (cos x)*(6sin x cos x)

Please find the 3rd, 4th and 5th derivatives.  Then try to recognize a pattern in the derivatives governed by the counter "n".