Rewrite the function y in exponential form.

Apply the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$.

$$\frac{dy}{dx} = \frac{3}{2}x^{\frac{3}{2}-1} = \frac{3}{2}x^{1/2}$$

Differentiate $\frac{dy}{dx}$ again using the power rule.

$$\frac{d^2y}{dx^2} = \frac{d}{dx}\left(\frac{3}{2}x^{1/2}\right) = \frac{3}{2} \cdot \frac{1}{2}x^{\frac{1}{2}-1}$$ $$\frac{d^2y}{dx^2} = \frac{3}{4}x^{-1/2}$$

$$\frac{d^2y}{dx^2} = \frac{3}{4\sqrt{x}}$$

The final answer is $\frac{3}{4\sqrt{x}}$.