Calc BC derivative problem with trig and double angle -- Help please

[jessieb128]

Homework Statement

Find f'(x) if f(x) = 8^(sin^2(3x))
Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it.

Homework Equations

if y=a^u then y' = ln a * a^u * du
sin(2x) = 2sinxcosx

The Attempt at a Solution

We're only on the second chapter so I'm not sure if we really need the first equation I gave, which is from the fifth chapter (but I'm in BC so maybe she expects us to know it already?). Still, using that equation I got f'(x) = ln 8 * 8^(sin^2(3x)) * 3sin6x

The 3sin6x came from when I took the derivative of sin^2(3x) and converted it from 6sin3xcos3x to 3sin6x

But I don't know how my teacher (an online teacher) wanted the answer to only have one trig function? Did I mess up somewhere?

 

[Chestermiller]

In terms of sin²θ, cos(2θ)=??