Question

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

Answer 1

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