Chapter 5, Problem 48RE

Define $F\left(x\right)$ by

$F\left(x\right)={\displaystyle {\int }_4^x\frac{1}{\sqrt{t}}dt}$

(a) Use Part $2$ of the Fundamental Theorem of Calculous to find $F^{\prime }\left(x\right)$ .

(b) Check the result in part (a) by first integrating and then differentiating.