指数関数
よって exp a {\displaystyle \exp _{a}} は各 a {\displaystyle a} に対し可逆で, exp a − 1 = log a . {\displaystyle \exp _{a}^{-1}=\log _{a}.}
( a x ) ′ = a x log  a . {\displaystyle (a^{x})'=a^{x}\log a.} 特に ( a x ) ′ | x = 0 = 1 {\displaystyle (a^{x})'|_{x=0}=1} となる a {\displaystyle a} を e {\displaystyle e} と書くと, ( e x ) ′ = e x . {\displaystyle (e^{x})'=e^{x}.}