To calculate the derivative of $f(x) = \frac{x^2 - 3x + 2}{1}$, we first simplify the function. Step 1: Simplify the function $f(x)$. Since any expression divided by 1 is itself, we have: $$ f(x) = x^2 - 3x + 2 $$ Step 2: Apply the power rule for differentiation. 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 $0$. Step 3: Combine the derivatives of each term. $$ f'(x) = 2x - 3 + 0 $$ $$ f'(x) = 2x - 3 $$ Step 4: Compare the result with the given options. 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 $\boxed{\text{c. } f'(x) = \frac{2x - 3}{1}}$. Last free one today — make it count tomorrow, or type /upgrade for unlimited.