1. **State the problem:** Find the derivative of the function $f(x) = x^3 - 5x + 2$ with respect to $x$. 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. - The derivative of a constant is 0. 3. **Apply the power rule to each term:** - Derivative of $x^3$ is $3x^{2}$. - Derivative of $-5x$ is $-5$. - Derivative of $2$ is $0$. 4. **Combine the results:** $$\frac{d}{dx}(x^3 - 5x + 2) = 3x^{2} - 5 + 0 = 3x^{2} - 5$$ 5. **Final answer:** The derivative of the function is $3x^{2} - 5$.