1. **State the problem:** Find the second derivative of the function $f(x) = x^3 + 5x$. 2. **Recall the first derivative:** From the previous problem, the first derivative is $f'(x) = 3x^{2} + 5$. 3. **Apply the derivative rules again:** - The derivative of $3x^{2}$ is $3 \times 2x^{1} = 6x$. - The derivative of the constant $5$ is $0$. 4. **Combine the results:** $$f''(x) = 6x + 0 = 6x$$ 5. **Interpretation:** The second derivative $f''(x)$ gives the rate of change of the slope of the tangent line, or the curvature of the function. **Final answer:** $$f''(x) = 6x$$