[b]미분계수와 대칭미분계수의 관계[br][/b][b]Relationship between derivatives and symmetric derivatives[/b][br][br]만약 [math]f'\left(a\right)[/math]가 존재하면 [math]\lim_{h\longrightarrow0}\frac{f\left(a+h\right)-f\left(a-h\right)}{2h}=f'\left(a\right)[/math]이다.[br]그러나 [math]f'\left(a\right)[/math]가 존재하지 않더라도 [math]\lim_{h\longrightarrow0}\frac{f\left(a+h\right)-f\left(a-h\right)}{2h}[/math]는 존재할 수 있다.[br]예: [math]f\left(x\right)=\left|x\right|[/math], [math]a=0[/math][br][br]If [math]f'\left(a\right)[/math] exists, then [math]\lim_{h\longrightarrow0}\frac{f\left(a+h\right)-f\left(a-h\right)}{2h}=f'\left(a\right)[/math].[br]However, even if [math]f'\left(a\right)[/math] does not exist, [math]\lim_{h\longrightarrow0}\frac{f\left(a+h\right)-f\left(a-h\right)}{2h}[/math] can exist.[br]Example: [math]f\left(x\right)=\left|x\right|[/math], [math]a=0[/math][br][br]Reference: https://en.wikipedia.org/wiki/Symmetric_derivative