Question

Найти полный дифференциал функции :
z =sin(x+3y).

Answer 1

$dz=z`_{x}dx+z`_{y}dy\\ \\ z`_{x}=(sin(x+3y))`_{x}=cos(x+3y)\cdot (x+3y)`_{x}=cos(x+3y)\cdot 1= cos(x+3y)\\ z`_{y}=(sin(x+3y))`_{y}=cos(x+3y)\cdot (x+3y)`_{y}=cos(x+3y)\cdot 3= 3cos(x+3y)\ \\ \\ dz=cos(x+3y)\cdot dx+3cos(x+3y)\cdot dy=cos(x+3y)\cdot(x+3y)$