Symmetric derivative
= Symmetric derivative
{title2=$f^s(x)=\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$}
The symmetric derivative compares values equally far to either side of a point. If the ordinary <derivative> exists, splitting the symmetric <difference quotient> into two ordinary <difference quotients> shows $f^s(x)=f'(x)$. The converse fails: the <absolute value function> has $f^s(0)=0$ but distinct left and right <one-sided derivatives> at zero.