1. The problem asks for the half derivative of the function $y=x$. 2. The half derivative is a fractional derivative of order $\frac{1}{2}$, which generalizes the concept of integer-order derivatives. 3. The formula for the half derivative of $x^n$ is given by: $$D^{1/2} x^n = \frac{\Gamma(n+1)}{\Gamma(n+1-\frac{1}{2})} x^{n-\frac{1}{2}}$$ where $\Gamma$ is the Gamma function. 4. For $y=x$, we have $n=1$. 5. Calculate the coefficients: $$\Gamma(2) = 1! = 1$$ $$\Gamma(1.5) = \frac{\sqrt{\pi}}{2}$$ 6. Substitute into the formula: $$D^{1/2} x = \frac{1}{\frac{\sqrt{\pi}}{2}} x^{\frac{1}{2}} = \frac{2}{\sqrt{\pi}} x^{\frac{1}{2}}$$ 7. Therefore, the half derivative of $y=x$ is: $$\boxed{D^{1/2} x = \frac{2}{\sqrt{\pi}} \sqrt{x}}$$