점 \(x=1\)에서 다음 함수의 미분계수를 구하라.
$$f(x)=\vert x \vert$$
풀이
\(\displaystyle f'(1)=\lim_{\Delta x\to0}\frac{f(1+\Delta x)-f(1)}{\Delta x}\)
\(\displaystyle=\lim_{\Delta x\to0}\frac{\vert 1+\Delta x \vert-\vert 1 \vert}{\Delta x}=\lim_{\Delta x\to0}\frac{1+\Delta x-1}{\Delta x}\)
\(\displaystyle=\lim_{\Delta x\to0}\frac{\Delta x}{\Delta x}=\lim_{\Delta x\to0}1=1\)