Question

Найти частные производные второго порядка функции многих переменных

Answer 1

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

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