Let `f(x)=x^3-3x^2+2x` Find `f'(x)`

Answer

To find the derivative \( f'(x) \) of the function \( f(x) = x^3 - 3x^2 + 2x \), we will apply the power rule of differentiation.

### Step-by-Step Solution:

1. **Identify the function**:
\[ f(x) = x^3 - 3x^2 + 2x \]

2. **Differentiate each term using the power rule**:
- The power rule states that if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \).

- Differentiate \( x^3 \):
\[ \frac{d}{dx}(x^3) = 3x^{3-1} = 3x^2 \]

- Differentiate \( -3x^2 \):
\[ \frac{d}{dx}(-3x^2) = -3 \cdot 2x^{2-1} = -6x \]

- Differentiate \( 2x \):
\[ \frac{d}{dx}(2x) = 2 \cdot 1x^{1-1} = 2 \]

3. **Combine the derivatives**:
\[ f'(x) = 3x^2 - 6x + 2 \]

### Final Answer:
\[ f'(x) = 3x^2 - 6x + 2 \]