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6.10: Más sobre Diferenciación Implícita. Extrema Condicional
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/6.10%3A_M%C3%A1s_sobre_Diferenciaci%C3%B3n_Impl%C3%ADcita._Extrema_Condicional
\[\begin{array}{l}{\sum_{j=1}^{n}\left[D_{j} f(\vec{p}, \vec{q})+\sum_{k=1}^{n} c_{k} D_{j} g_{k}(\vec{p}, \vec{q})\right] D_{i} H_{j}(\vec{q})} \\ {\qquad+D_{n+i} f(\vec{p}, \vec{q})+\sum_{k=1}^{n} c... $\begin{array}{l}{\sum_{j=1}^{n}\left[D_{j} f(\vec{p}, \vec{q})+\sum_{k=1}^{n} c_{k} D_{j} g_{k}(\vec{p}, \vec{q})\right] D_{i} H_{j}(\vec{q})} \\ {\qquad+D_{n+i} f(\vec{p}, \vec{q})+\sum_{k=1}^{n} c_{k} D_{n+i} g_{k}(\vec{p}, \vec{q})=0, \quad i \leq m}. \end{array}$ $\begin{array}{l}{\qquad \begin{aligned}-\frac{2}{a}[d x d y+d x d z+& d y d z-(d x+d y+d z)^{2} ] \\=& \frac{1}{a}\left[d x^{2}+d y^{2}+d z^{2}+(d x+d y+d z)^{2}\right]=d^{2} F. \end{aligned}}\end{array}$

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