CoV15

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Compute the first variation of J(y)=e^{{y(a)}}\,

\delta J(y,h)\,={\frac  {d}{d\varepsilon }}J(y+\varepsilon h)\left.\right|_{{\varepsilon =0}}
={\frac  {d}{d\varepsilon }}e^{{(y+\varepsilon h)(a)}}\left.\right|_{{\varepsilon =0}}
={\frac  {d}{d\varepsilon }}e^{{y(a)+\varepsilon h(a)}}\left.\right|_{{\varepsilon =0}}
=e^{{y(a)+\varepsilon h(a)}}\cdot h(a)\left.\right|_{{\varepsilon =0}}
=e^{{y(a)}}\cdot h(a)


Main Page : Calculus of Variations