Hello everyone, any assistance would be greatly appreciated.

Let $\displaystyle f(x)$ $\displaystyle =$ $\displaystyle 12xsinxcosx$ . Find $\displaystyle f'(\frac{-3\pi}{2})$.

I attempt to differentiate the function using the product rule:

I use the product rule for $\displaystyle sinx cosx$

$\displaystyle sinx(-sinx)+cosx(cosx)=-sin^2x+cos^2x$

And then $\displaystyle 12x(-sin^2x+cos^2x)$

$\displaystyle =12x(-1)+(-sin^2x+cos^2x)(12)$

$\displaystyle =-12x-12sin^2x+12cos^2x$

Using the derivative of $\displaystyle f(x)$, I try to evaluate $\displaystyle f'(\frac{-3\pi}{2})$.

$\displaystyle -12(\frac{-3\pi}{2})-12sin^2(\frac{-3\pi}{2})+12cos^2(\frac{-3\pi}{2})$

I end up getting $\displaystyle 18\pi-12$

However, the book answer is just $\displaystyle 18\pi$.

Can someone tell me where I went wrong? Thanks in advance.