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

Explanation

To evaluate the derivative of the function \(3x^2\) with respect to \(x\), we will follow the rules of differentiation. Here’s a step-by-step solution:

### Step 1: Identify the function
The function we need to differentiate is:
\[ f(x) = 3x^2 \]

### Step 2: Apply the constant multiple rule
According to the constant multiple rule of differentiation, if you have a constant multiplied by a function, you can take the constant out of the derivative. Therefore, we can express the derivative as:
\[ \frac{d}{dx}(3x^2) = 3 \cdot \frac{d}{dx}(x^2) \]

### Step 3: Differentiate \(x^2\)
Next, we apply the power rule of differentiation. The power rule states that if \(f(x) = x^n\), then:
\[ \frac{d}{dx}(x^n) = n \cdot x^{n-1} \]
In our case, \(n = 2\). Thus:
\[ \frac{d}{dx}(x^2) = 2 \cdot x^{2-1} = 2x \]

### Step 4: Combine the results
Substituting back into our expression from Step 2, we have:
\[ \frac{d}{dx}(3x^2) = 3 \cdot (2x) = 6x \]

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

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