Question

Найти частные производные второго порядка функции многих переменных

Answer 1

$\frac{\partial u}{\partial x}=\ln(y+z),\,\frac{\partial^2 u}{\partial x^2}=0,\, \frac{\partial^2 u}{\partial x\partial y}=\frac{1}{y+z},\, \frac{\partial^2 u}{\partial x\partial z}=\frac{1}{y+z},\\\frac{\partial u}{\partial y}=\frac{x}{y+z},\, \frac{\partial^2 u}{\partial y^2}=-\frac{x}{(y+z)^2},\,\frac{\partial^2 u}{\partial y\partial x}=\frac{\partial^2 u}{\partial x\partial y}=\frac{1}{y+z},\,\frac{\partial^2 u}{\partial y\partial z}=-\frac{x}{(y+z)^2},$

$\frac{\partial u}{\partial z}=\frac{x}{y+z},\, \frac{\partial^2 u}{\partial z^2}=-\frac{x}{(y+z)^2},\,\frac{\partial^2 u}{\partial z\partial x}=\frac{\partial^2 u}{\partial x\partial z}=\frac{1}{y+z},\,\frac{\partial^2 u}{\partial z\partial y}=\frac{\partial^2 u}{\partial y\partial z}=-\frac{x}{(y+z)^2},$