1. Problem: Find the derivative $f'(x)$ if $f(x) = 8x^3 + 9x^2 - 5$. 2. Formula: The derivative of $x^n$ is $nx^{n-1}$. 3. Step-by-step: - Derivative of $8x^3$ is $8 \times 3x^{3-1} = 24x^2$. - Derivative of $9x^2$ is $9 \times 2x^{2-1} = 18x$. - Derivative of constant $-5$ is $0$. 4. Combine results: $$f'(x) = 24x^2 + 18x$$ 5. Explanation: We apply the power rule to each term separately and sum the results. Final answer: $$\boxed{f'(x) = 24x^2 + 18x}$$