Find the derivative of $\displaystyle y = (tan(8x))^2$.

Here is what I did, but apparently it's incorrect:

$\displaystyle y' = \frac {dy}{du} \frac{du}{dx} = [\frac{d}{du}u^2][\frac{d}{dx} tan 8x]$

$\displaystyle =2[tan 8x][8][\sec ^2 x]$

$\displaystyle =16[tan 8x][\sec ^2 x]$