Evaluate:
`(d)/(dx)(x^(1//2))`

Explanation

To evaluate the derivative of the function \( y = x^{1/2} \), we will follow the steps of differentiation using the power rule.

### Step-by-Step Solution:

1. **Identify the function**: We have the function \( y = x^{1/2} \).

2. **Apply the power rule**: The power rule states that if \( y = x^n \), then the derivative \( \frac{dy}{dx} \) is given by:
\[ \frac{dy}{dx} = n \cdot x^{n-1} \]
In our case, \( n = \frac{1}{2} \).

3. **Differentiate**: Substitute \( n \) into the power rule:
\[ \frac{dy}{dx} = \frac{1}{2} \cdot x^{\frac{1}{2} - 1} \]

4. **Simplify the exponent**: Calculate \( \frac{1}{2} - 1 \):
\[ \frac{1}{2} - 1 = -\frac{1}{2} \]
So we have:
\[ \frac{dy}{dx} = \frac{1}{2} \cdot x^{-\frac{1}{2}} \]

5. **Rewrite the result**: The expression \( x^{-\frac{1}{2}} \) can be rewritten as \( \frac{1}{\sqrt{x}} \):
\[ \frac{dy}{dx} = \frac{1}{2\sqrt{x}} \]

### Final Result:
Thus, the derivative of \( y = x^{1/2} \) is:
\[ \frac{dy}{dx} = \frac{1}{2\sqrt{x}} \]