CoV15

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

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

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