Problem
Let $g(x)=\int_{4}^{x}(5+\sqrt{t}) d t$. Find $g^{\prime}(x)$. \[ g^{\prime}(x)= \]
Solution
Step 1 ：Let $g(x)=\int_{4}^{x}(5+\sqrt{t}) d t$.
Step 2 ：By the Fundamental Theorem of Calculus, the derivative of the integral of a function from a constant to x is just the function evaluated at x.
Step 3 ：So, $g^{\prime}(x)=5+\sqrt{x}$.
Step 4 ：Therefore, the final answer is \(\boxed{g^{\prime}(x)=5+\sqrt{x}}\).
