(\partial ^2)/(\partial x\partial y)(({F}(x,y))(3x^2-6y^3+4xy-10))

Решение

\frac{\partial ^{2}}{\partial x \partial y} ((F (x, y)) (3 x^{2} - 6 y^{3} + 4 x y - 10))

(\frac{\partial}{\partial y} (\frac{\partial}{\partial x} (F (x, y))) (3 x^{2} - 6 y^{3} + 4 x y - 10) + (- 18 y^{2} + 4 x) \frac{\partial}{\partial x} (F (x, y))) + (4 F (x, y) + \frac{\partial}{\partial y} (F (x, y)) (6 x + 4 y))

Шаги решения

\frac{\partial ^{2}}{\partial x \partial y} ((F (x, y)) (3 x^{2} - 6 y^{3} + 4 x y - 10))

\frac{\partial}{\partial x} (F (x, y) (3 x^{2} - 6 y^{3} + 4 x y - 10)) = \frac{\partial}{\partial x} (F (x, y)) (3 x^{2} - 6 y^{3} + 4 x y - 10) + (6 x + 4 y) F (x, y)

= \frac{\partial}{\partial y} (\frac{\partial}{\partial x} (F (x, y)) (3 x^{2} - 6 y^{3} + 4 x y - 10) + (6 x + 4 y) F (x, y))

\frac{\partial}{\partial y} (\frac{\partial}{\partial x} (F (x, y)) (3 x^{2} - 6 y^{3} + 4 x y - 10) + (6 x + 4 y) F (x, y)) = (\frac{\partial}{\partial y} (\frac{\partial}{\partial x} (F (x, y))) (3 x^{2} - 6 y^{3} + 4 x y - 10) + (- 18 y^{2} + 4 x) \frac{\partial}{\partial x} (F (x, y))) + (4 F (x, y) + \frac{\partial}{\partial y} (F (x, y)) (6 x + 4 y))

= (\frac{\partial}{\partial y} (\frac{\partial}{\partial x} (F (x, y))) (3 x^{2} - 6 y^{3} + 4 x y - 10) + (- 18 y^{2} + 4 x) \frac{\partial}{\partial x} (F (x, y))) + (4 F (x, y) + \frac{\partial}{\partial y} (F (x, y)) (6 x + 4 y))