詳解：(1)設 \(f(x) = \sqrt x \) ， \(f'(x) = \frac{1}{{2\sqrt x }}\)

(2)微分公式 \(f(x + \Delta x) \buildrel\textstyle.\over= f(x) + f'(x)\Delta x\)

(3)令 \(x = 100\) ， \(\Delta x = 0.01\)  \(f(100 + 0.01) \buildrel\textstyle.\over= f(100) + f'(100)0.01\)

\(\sqrt {100.01}  \buildrel\textstyle.\over= 10 + \frac{1}{{20}}0.01 = 10.0005\)