Evaluate:
`(d)/(dx)(3x^(2))`

Explanation

To evaluate the derivative of the function \(3x^2\) with respect to \(x\), we will follow these steps:

### Step-by-step Solution:

1. **Identify the function to differentiate**:
We need to differentiate the function \(f(x) = 3x^2\).

2. **Apply the constant multiple rule**:
Since \(3\) is a constant, we can factor it out of the differentiation. Thus, we rewrite the differentiation as:
\[ \frac{d}{dx}(3x^2) = 3 \cdot \frac{d}{dx}(x^2) \]

3. **Use the power rule for differentiation**:
The power rule states that if \(f(x) = x^n\), then \(\frac{d}{dx}(x^n) = n \cdot x^{n-1}\). Here, \(n = 2\). Therefore, we can apply the power rule:
\[ \frac{d}{dx}(x^2) = 2 \cdot x^{2-1} = 2x \]

4. **Combine the results**:
Now substitute back into the equation from step 2:
\[ \frac{d}{dx}(3x^2) = 3 \cdot (2x) = 6x \]

5. **Final answer**:
Thus, the derivative of \(3x^2\) with respect to \(x\) is:
\[ \frac{d}{dx}(3x^2) = 6x \]