Answer
a) $ f′(x)=\dfrac{1}{2\sqrt x}$
b) $\dfrac{1}{12}, \dfrac{1}{18}$
Work Step by Step
a) Now, $ f′(x)=\lim_\limits{ h\to 0} \dfrac{f(x+h)-f(x)}{h}$
or, $=\lim_\limits{ h\to 0} \dfrac{\sqrt{x+h}-\sqrt x}{h}$
or, $=\lim_\limits{ h\to 0} \dfrac{1}{\sqrt{x+h}+\sqrt x}$
or, $=\dfrac{1}{\sqrt{x+0}+\sqrt x}$
or, $ f′(x)=\dfrac{1}{2\sqrt x}$
b) $ f′(36)=\dfrac{1}{2 \sqrt{36}}=\dfrac{1}{12}$
and $ f′(81)=\dfrac{1}{2 \sqrt{81}}=\dfrac{1}{18}$
