Find the derivative at x = 2 of the function `f(x)=4x`.

Answer

To find the derivative of the function \( f(x) = 4x \) at \( x = 2 \), we will follow these steps:

### Step 1: Write down the function
The function given is:
\[ f(x) = 4x \]

### Step 2: Differentiate the function
To find the derivative \( f'(x) \), we differentiate \( f(x) \) with respect to \( x \):
\[ f'(x) = \frac{d}{dx}(4x) \]

### Step 3: Apply the constant multiple rule
The derivative of \( 4x \) can be calculated using the constant multiple rule, which states that the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function. Here, the constant is 4, and the derivative of \( x \) with respect to \( x \) is 1:
\[ f'(x) = 4 \cdot \frac{d}{dx}(x) = 4 \cdot 1 = 4 \]

### Step 4: Evaluate the derivative at \( x = 2 \)
Since we found that \( f'(x) = 4 \), which is a constant, the value of the derivative at any point, including \( x = 2 \), is:
\[ f'(2) = 4 \]

### Final Answer
Thus, the derivative of the function \( f(x) = 4x \) at \( x = 2 \) is:
\[ \boxed{4} \]