Simplify the function f(x).

Since any expression divided by 1 is itself, we have:

$$f(x) = x^2 - 3x + 2$$

The power rule states that $\frac{d}{dx}(x^n) = nx^{n-1}$. The derivative of a constant term is 0.
We differentiate each term of $f(x)$:

• The derivative of $x^2$ is $2x^{2-1} = 2x$.
• The derivative of $-3x$ is $-3 \cdot 1 \cdot x^{1-1} = -3x^0 = -3 \cdot 1 = -3$.
• The derivative of the constant 2 is 0.

$$f'(x) = 2x - 3 + 0$$ $$f'(x) = 2x - 3$$

a. $f'(x) = \frac{2x - 3}{x^2}$
b. $f'(x) = \frac{x^2 - 3}{x^2}$
c. $f'(x) = \frac{2x - 3}{1}$
d. $f'(x) = \frac{x^2 - 3}{x} - 1$

Our calculated derivative $2x - 3$ matches option c, as $\frac{2x - 3}{1}$ simplifies to $2x - 3$.

The final answer is $\boxed{\text{c. } f'(x) = \frac{2x - 3}{1}}$.