AP DSC School Assistant Math Model Test 3

Concept:The problem requires finding the derivative of a function that is a sum of an exponential term and a product. Use the derivative of $a^x$ (which is $a^x \ln a$) and the product rule for $x \log x$ (where $\log$ is natural log).Explanation:Given $y = 2^{x} + x \log x$.Differentiate each term separately:1. $\frac{d}{dx}(2^{x}) = 2^{x} \log 2$   (since $\log$ base $e$).2. For $x \log x$, apply the product rule: $\frac{d}{dx}(x) \cdot \log x + x \cdot \frac{d}{dx}(\log x) = 1 \cdot \log x + x \cdot \frac{1}{x} = \log x + 1$.Adding both results: $\frac{dy}{dx} = 2^{x} \log 2 + \log x + 1$.Answer:The correct option is B ($2^{x} \log 2 + \log x + 1$).