Pretty simple question.
This definition of the Gateaux Derivative presents it as: \begin{equation} df(u,\psi)=\dfrac{d}{d\epsilon}f(u+\epsilon\psi)\Bigg{|}_{\epsilon=0} \end{equation} Why is the derivative being evaluated at $\epsilon=0$ in that definition? The fact that I'm interpreting it in a rather similar way as the directional derivative is causing some confusion.