![{\displaystyle {\frac {\operatorname {d} ^{2}S}{\operatorname {d} x^{2}}},\quad {\frac {\operatorname {d} ^{2}S}{\operatorname {d} x\operatorname {d} y}},\quad {\frac {\operatorname {d} ^{2}S}{\operatorname {d} y^{2}}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ec473c12dad06e553f0abfbbfce2cde49e378a9)
dans le troisième, quatre ; savoir,
![{\displaystyle {\frac {\operatorname {d} ^{3}S}{\operatorname {d} x^{3}}},\quad {\frac {\operatorname {d} ^{3}S}{\operatorname {d} x^{2}\operatorname {d} y}},\quad {\frac {\operatorname {d} ^{3}S}{\operatorname {d} x\operatorname {d} y^{2}}},\quad {\frac {\operatorname {d} ^{3}S}{\operatorname {d} y^{3}}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/20077dfe5c78b8bc92dd89c0efee9dceda5a00b5)
et ainsi de suite, c’est-à-dire, en général,
pour n.ième ordre, savoir ;
![{\displaystyle {\frac {\operatorname {d} ^{n}S}{\operatorname {d} x^{n}}},\ {\frac {\operatorname {d} ^{n}S}{\operatorname {d} x^{n-1}\operatorname {d} y}},\ {\frac {\operatorname {d} ^{n}S}{\operatorname {d} x^{n-2}\operatorname {d} y^{2}}},\ldots {\frac {\operatorname {d} ^{n}S}{\operatorname {d} x^{2}\operatorname {d} y^{n-2}}},\ {\frac {\operatorname {d} ^{n}S}{\operatorname {d} x\operatorname {d} y^{n-1}}},\ {\frac {\operatorname {d} ^{n}S}{\operatorname {d} y^{n}}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/772cdcc745db4b1ac8902e5db9eb23db4d6b2b21)
S’il s’agit d’une fonction de trois variables, elle aura, dans le premier ordre, trois coefficiens différentiels, savoir :
![{\displaystyle {\frac {\operatorname {d} S}{\operatorname {d} x}},\qquad {\frac {\operatorname {d} S}{\operatorname {d} y}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8092969e4dab9daef54b2d7a98d18b8997007de7)
![{\displaystyle {\frac {\operatorname {d} S}{\operatorname {d} z}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60f57aba5a033ec8c6f29faab5e685060fdfe0e2)
dans le second, six ; savoir :
![{\displaystyle {\frac {\operatorname {d} ^{2}S}{\operatorname {d} x^{2}}},\qquad {\frac {\operatorname {d} ^{2}S}{\operatorname {d} x\operatorname {d} y}},\qquad {\frac {\operatorname {d} ^{2}S}{\operatorname {d} y^{2}}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d9ed1d32cbce13009cf503131867daa954a62c)
![{\displaystyle {\frac {\operatorname {d} ^{2}S}{\operatorname {d} x\operatorname {d} z}},\qquad {\frac {\operatorname {d} ^{2}S}{\operatorname {d} y\operatorname {d} z}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1181862298d8b70ba82af3545480d844a054865)
![{\displaystyle {\frac {\operatorname {d} ^{2}S}{\operatorname {d} z^{2}}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e76f5610421f8d626f4106239c458e2f73739aa2)
dans le troisième, dix ; savoir :