편집토론역사ACL수식 문법 테스트분류테스트아무 수학 공식이나 적어보세요. 수식 문법을 테스트하기 위해 만든 문서입니다.f′(x)=(x+x+⋯+x⏞x times)′=limh→ 0{(x+h)+(x+h)+⋯+(x+h)⏞(x+h) times}−(x+x+⋯+x⏞x times)h=limh→ 0(h+h+⋯+h)⏞x times+{(x+h)+(x+h)+⋯+(x+h)⏞h times}h=x+limh→ 0(xh+h2)h=x+x=2x\begin{aligned}f'(x)&=(\overbrace{x+x+ \cdots +x}^{x\;\rm{times}})'\\&= \displaystyle\lim_{h \to \ 0} \frac {\{\overbrace{(x+h)+(x+h)+ \cdots +(x+h)}^{(x+h)\;\rm{times}}\} - (\overbrace{x+x+ \cdots +x}^{x\;\rm{times}})}{h}\\&= \displaystyle\lim_{h \to \ 0} \frac {(\overbrace{h+h+ \cdots +h)}^{x\;\rm{times}} + \{\overbrace{(x+h)+(x+h)+ \cdots +(x+h)}^{h\;\rm{times}}\}}{h}\\&=x +\displaystyle\lim_{h \to \ 0} \frac{(xh+h^2)}{h}\\&=x+x=2x\end{aligned}f′(x)=(x+x+⋯+xxtimes)′=h→ 0limh{(x+h)+(x+h)+⋯+(x+h)(x+h)times}−(x+x+⋯+xxtimes)=h→ 0limh(h+h+⋯+h)xtimes+{(x+h)+(x+h)+⋯+(x+h)htimes}=x+h→ 0limh(xh+h2)=x+x=2xlimx→af(x)=L\displaystyle \lim_{ x \rightarrow a }{ f ( x ) } = L x→alimf(x)=L