$12(3-2x)^{-3}$
$x(4x^2-3)^{1/2}$
For 1, I only need the power rule to differentiate it . Whereas for 2, I need to apply both power and product rule to differentiate it .
Sorry for the misconception as I just started learning differentiation !!
$$\frac{d}{dx}\left[x\sqrt{4x^2-3}\right] = x\left[\frac 12\left(4x^2 -3\right)^{-\frac 12}(8x)\right] + \sqrt{4x^2-3}$$ $$=\frac{4x^2 + 4x^2 - 3}{\sqrt{4x^2 - 3}}=\frac{8x^2 - 3}{\sqrt{4x^2 - 3}}$$
I do not understand how is there an addition of $\sqrt{4x^2 -3}$ in the second step . The first part is applying the power rule and I understand that .
It would help to be very explicit with each step. By the product rule: $$\frac{d}{dx}\left[x\sqrt{4x^2 - 3}\right] = x\cdot\left(\frac d{dx} \sqrt{4x^2-3}\right) + \left(\frac{d}{dx} x\right)\cdot \sqrt{4x^2-3}$$ I assume that you know what $\frac d{dx}(x)$ is, and this should close the misconception.