Chapter 11 - 11.5 - The Binomial Theorem - 11.5 Exercises - Page 813: 65

$=\frac{1}{(\sqrt{x+h}+\sqrt x)}$

$\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{x+h}-\sqrt x}{h}=\frac{(\sqrt{x+h}-\sqrt x)(\sqrt{x+h}+\sqrt x))}{h(\sqrt{x+h}+\sqrt x)}=\frac{(x+h)-x}{h(\sqrt{x+h}+\sqrt x)}=\frac{h}{h(\sqrt{x+h}+\sqrt x)}=\frac{1}{(\sqrt{x+h}+\sqrt x)}$