1. **State the problem:** Find the derivative of the function $g(x) = x^3 - 3x^2 + 2$. 2. **Recall the derivative rules:** - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of a constant is 0. - The derivative of a sum/difference is the sum/difference of the derivatives. 3. **Apply the power rule to each term:** - Derivative of $x^3$ is $3x^{2}$. - Derivative of $-3x^2$ is $-3 \times 2x^{1} = -6x$. - Derivative of $2$ is $0$. 4. **Combine the results:** $$g'(x) = 3x^{2} - 6x + 0 = 3x^{2} - 6x$$ 5. **Final answer:** $$\boxed{g'(x) = 3x^{2} - 6x}$$