Gateux derivative
\[\begin{aligned}
D_hf(x)&=\lim_{\epsilon\rightarrow 0}\frac{f(x+ \epsilon h)-f(x)}{ \epsilon }\\
&=\lim_{ \epsilon \rightarrow 0}\frac{\frac{\partial f(x+ \epsilon h)}{\partial \epsilon }}{1}\\
&=\frac{d }{d \epsilon }f(x+ \epsilon h)|_{ \epsilon =0}
\end{aligned}\]
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