Question

Найти полный дифференциал функции u=3x^2+5y^4-7z

Answer 1

$U=3x^2+5y^4-7z \\ dU=2*3xdx+5*4y^3dy-7dz=6xdx+20y^3dy-7dz \\$

Answer 2

$u=3x^2+5y^4-7z\\\frac{\partial u}{\partial x}=3*2x+0-0=6x\\\frac{\partial u}{\partial y}=0+5*4y^3-0=20y^3\\\frac{\partial u}{\partial z}=0+0-7=-7\\du=\frac{\partial u}{\partial x}dx+\frac{\partial u}{\partial y}dy+\frac{\partial u}{\partial z}dz=6xdx+20y^3dy-7dz$