Найти частные производные первого и второго порядка функции трех переменных U=xln(y+z)...

Решите задачу:

$U=x\cdot ln(y+z)\\\\U'_{x}=ln(y+z)\\\\U'_{y}=x\cdot \frac{1}{y+z}\\\\U'_{z}=x\cdot \frac{1}{y+z}\\\\U''_{xx}=(ln(y+z))'_{x}=0\\\\U''_{xy}=(ln(y+z))'_{y}=\frac{1}{y+z}\\\\U''_{xz}=(ln(y+z))'_{z}=\frac{1}{y+z}\\\\U''_{yy}=(\frac{x}{y+z})'_{y}=-\frac{x}{(y+z)^2}\\\\U''_{yx}=(\frac{x}{y+z})'_{x}=\frac{1}{y+z}\\\\U''_{yz}=(\frac{x}{y+z})'_{z}=-\frac{x}{(y+z)^2}\\\\U''_{zz}=(\frac{x}{y+z})'_{z}=-\frac{x}{(y+z)^2}\\\\U''_{zx}=( \frac{x}{y+z})'_{x}=\frac{1}{y+z}$

$U''_{zy}=( \frac{x}{y+z})'_{y} =-\frac{x}{(y+z)^2}$