Answer
$\frac{dy}{dx} = 12x^{3}$
Work Step by Step
$\frac{dy}{dx} = \frac{dy}{du}*\frac{du}{dx}$
Now,
$\frac{dy}{du} = \frac{d(6u-9)}{du} = 6$
And,
$\frac{du}{dx} = \frac{d (\frac{1}{2})x^{4}}{dx} = 2x^{3}$
Now,
$\frac{dy}{dx} = 12x^{3}$