If `f(x) = x^(2) - 2x` then find the derivative of this function.

Answer

To find the derivative of the function \( f(x) = x^2 - 2x \), we will use the rules of differentiation.

### Step-by-Step Solution:

1. **Identify the function**:
\[ f(x) = x^2 - 2x \]

2. **Apply the power rule of differentiation**:
The power rule states that if \( f(x) = x^n \), then \( f'(x) = nx^{n-1} \).

3. **Differentiate each term**:
- For the first term \( x^2 \):
\[ \frac{d}{dx}(x^2) = 2x^{2-1} = 2x \]
- For the second term \( -2x \):
\[ \frac{d}{dx}(-2x) = -2 \cdot \frac{d}{dx}(x) = -2 \cdot 1 = -2 \]

4. **Combine the derivatives**:
\[ f'(x) = 2x - 2 \]

5. **Final result**:
\[ f'(x) = 2x - 2 \]

### Summary:
The derivative of the function \( f(x) = x^2 - 2x \) is:
\[ f'(x) = 2x - 2 \]