Question

Найти полный дифференциал функций
1) z=2x³+xy
2) z=x³-2xy²

Answer 1

1.

$z = 2 {x}^{3} + xy$

$Z'_x = 6 {x}^{2} + y \\ Z'_y = x \\ dz = (6 {x}^{2} + y)dx + xdy$

2.

$z = {x}^{3} - 2x {y}^{2}$

$Z'_x = 3 {x}^{2} - 2 {y}^{2} \\ Z'_y = - 4xy \\ dz = (3 {x}^{2} - 2 {y}^{2}) dx - 4xydy$