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6.1: Derivadas direccionales y parciales
https://espanol.libretexts.org/Matematicas/Analisis/Libro%3A_An%C3%A1lisis_matem%C3%A1tico_(Zakon)/06%3A_Diferenciaci%C3%B3n_en_Ey_Otros_Espacios_Lineales_Normados/6.01%3A_Derivadas_direccionales_y_parciales
\[\begin{aligned} D_{\vec{u}} f\left(\vec{x}_{0}\right) &=\lim _{t \rightarrow 0} \frac{1}{t}\left[f\left(\vec{x}_{0}+t \vec{u}\right)-f\left(\vec{x}_{0}\right)\right] \\ &=\lim _{t \rightarrow 0} \fr... $\begin{aligned} D_{\vec{u}} f\left(\vec{x}_{0}\right) &=\lim _{t \rightarrow 0} \frac{1}{t}\left[f\left(\vec{x}_{0}+t \vec{u}\right)-f\left(\vec{x}_{0}\right)\right] \\ &=\lim _{t \rightarrow 0} \frac{1}{t}\left[f\left(\vec{p}+t_{0} \vec{u}+t \vec{u}\right)-f\left(\vec{p}+t_{0} \vec{u}\right)\right] \\ &=\lim _{t \rightarrow 0} \frac{1}{t}\left[h\left(t_{0}+t\right)-h\left(t_{0}\right)\right] \\ &=h^{\prime}\left(t_{0}\right) . \quad \text {(Explain!)} \end{aligned}$

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