1. **State the problem:** Find the derivative $f'(x)$ of the function $f(x) = x^3 - 3x + 1$. 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 $-3x$ is $-3$. - Derivative of $1$ is $0$. 4. **Combine the results:** $$f'(x) = 3x^{2} - 3 + 0 = 3x^{2} - 3$$ 5. **Final answer:** $$f'(x) = 3x^{2} - 3$$