Differentiate using Function of a Function (Chain Rule)

Is this correct?

$\displaystyle (x^9-8)^6$

$\displaystyle u=x^9-2$

$\displaystyle du/dx=9x^8$

$\displaystyle y=u^6$

$\displaystyle dy/du=6u^5$

$\displaystyle dy/dx=dy/du . du/dx$

$\displaystyle dy/dx = 6(x^9-2)^5 . 9x^8$