Answer
$\frac{dy}{dx} = \frac{3x-2}{\sqrt {3x^{2} - 4x +6}} $
Work Step by Step
$y = \sqrt u$
where,
$u = 3x^{2} - 4x +6$
Now,
$\frac{dy}{du} = \frac{1}{2 \sqrt u} $
and,
$\frac{du}{dx} = 6x -4$
So,
$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$
$\frac{dy}{dx} = \frac{1}{2 \sqrt u} \times (6x-4)$
$\frac{dy}{dx} = \frac{1}{\sqrt (3x^{2} - 4x +6)} \times (3x-2)$
