Задача 72154 Найти частные производные функции....
Условие
Решение
[m]z`_{y}=(x^2sin(y+4))`_{y}=x^2\cdot (sin(y+4))`_{y}=x^2\cdot (cos(y+4))\cdot (y+4)`_{y}=x^2cos(y+4)[/m]
[m]z``_{xx}=(z`_{x})`_{x}=(2x\cdot sin(y+4))`_{x}=2sin(y+4)\cdot (x)`=2sin(y+4)[/m]
[m]z``_{xy}=(z`_{x})`_{y}=(2x\cdot sin(y+4))`_{y}=2x\cdot (sin(y+4))`_{y}=2x\cdot (cos(y+4))\cdot (y+4)`_{y}=2x\cdot cos(y+4)[/m]
[m]z``_{yy}=(z`_{y})`_{y}=(x^2cos(y+4))`_{y}=x^2\cdot (-sin(y+4))\cdot (y+4)`_{y}=x^2\cdot (-sin(y+4))=-x^2\cdot sin(y+4)[/m]
[m]z``_{yx}=(z`_{y})`_{x}=(x^2cos(y+4))`_{x}=cos(y+4)\cdot (x^2)`_{x}=cos(y+4)\cdot (2x)=2x\cdot cos(y+4)[/m]
[m]z``_{xy}=z``_{yx}=2x\cdot cos(y+4)[/m]