1. **State the problem:** We are given the function $f(x) = \frac{1}{3}x^3 - x^2$ and need to find its derivative $f'(x)$. 2. **Recall the derivative rules:** - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of a constant times a function is the constant times the derivative of the function. 3. **Apply the power rule to each term:** - For $\frac{1}{3}x^3$, the derivative is $\frac{1}{3} \times 3x^{3-1} = \frac{1}{3} \times 3x^2$. - For $-x^2$, the derivative is $-2x^{2-1} = -2x$. 4. **Simplify the derivative:** $$f'(x) = \frac{1}{3} \times 3x^2 - 2x = \cancel{\frac{1}{3} \times 3}x^2 - 2x = x^2 - 2x$$ 5. **Final answer:** $$f'(x) = x^2 - 2x$$