In applied mathematics and the calculus of variations, the first variation of a functional J is defined as the linear functional δ J {\displaystyle \delta J} mapping the function h to δ J = lim ε → 0 J − J ε = d d ε J | ε = 0, {\displaystyle \delta J=\lim _{\varepsilon \to 0}{\frac {J-J}{\varepsilon }}=\left.{\frac {d}{d\varepsilon }}J\right|_{\varepsilon =0},} where y and h are functions, and ε is a scalar. Wikipedia