1. The problem asks for the derivative of the sum of two functions $f(x)$ and $g(x)$ according to the Sum Rule. 2. The Sum Rule in calculus states that the derivative of a sum of functions is the sum of their derivatives. 3. Mathematically, this is expressed as: $$\frac{d}{dx}[f(x) + g(x)] = f'(x) + g'(x)$$ 4. This means you differentiate each function separately and then add the results. 5. Let's examine the options: - a. $f(x)g'(x) + g(x)f'(x)$ is the product rule, not the sum rule. - b. $\frac{f'(x)}{g'(x)}$ is a quotient, not related to the sum rule. - c. $f'(x) + g'(x)$ matches the sum rule. - d. $f(g'(x))$ is a composition, not the sum rule. 6. Therefore, the correct answer is option c: $f'(x) + g'(x)$. Final answer: c. $f'(x) + g'(x)$