(1 point) Differentiate g(x)=11sqrt (x)cdot e^x Answer: g'(x)=

To differentiate the function \( g(x) = 11\sqrt{x} \cdot e^x \), we will use the product rule. The product rule states that if you have a function \( h(x) = f(x) \cdot g(x) \), then its derivative is given by: Here, let \( f(x) = 11\sqrt{x} \) and \( g(x) = e^x \).First, we need to find the derivatives of \( f(x) \) and \( g(x) \):1. \( f(x) = 11\sqrt{x} = 11x^{1/2} \) 2. \( g(x) = e^x \) Now, apply the product rule: Combine the terms: To combine these terms, express them with a common denominator: Thus, the derivative of \( g(x) = 11\sqrt{x} \cdot e^x \) is: