The problem is:

\(\displaystyle p(x) = sin^3(pi*x)\)

Chain rule states:

\(\displaystyle f'(g(x))g'(x)\)

From this problem, I noted:

\(\displaystyle f(x) = sin^3(x)\)

\(\displaystyle f'(x) = 3sin^2(x)\)

\(\displaystyle g(x) = pi*x\)

\(\displaystyle g'(x) = pi\)

So applying these to the chain rule, we get:

\(\displaystyle 3sin^2(pi*x) * (pi)\)

But this doesn't seem to be the correct answer. I've applied the same methodology for other problems and the chain rule seems to work there, but not here. Does anyone know what I'm doing wrong? Any help would be appreciated. Thanks.