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

Explanation

To evaluate the derivative of \( x^{1/2} \) with respect to \( x \), we can follow these steps:

### Step 1: Identify the function to differentiate
We need to differentiate the function \( f(x) = x^{1/2} \).

### Step 2: Apply the power rule of differentiation
The power rule states that if \( f(x) = x^n \), then the derivative \( f'(x) \) is given by:
\[ f'(x) = n \cdot x^{n-1} \]
In our case, \( n = \frac{1}{2} \).

### Step 3: Differentiate using the power rule
Using the power rule, we differentiate \( f(x) = x^{1/2} \):
\[ \frac{d}{dx}(x^{1/2}) = \frac{1}{2} \cdot x^{(1/2) - 1} = \frac{1}{2} \cdot x^{-1/2} \]

### Step 4: Simplify the expression
The expression \( x^{-1/2} \) can be rewritten in terms of a square root:
\[ \frac{1}{2} \cdot x^{-1/2} = \frac{1}{2 \sqrt{x}} \]

### Final Answer
Thus, the derivative of \( x^{1/2} \) with respect to \( x \) is:
\[ \frac{1}{2 \sqrt{x}} \]

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