Question

Найти полный дифференциал функции

Answer 1

Ответ:

$Z'x = {e}^{ {x}^{2} - {y}^{3} + 9 } \times 2x$

$Z'y = {e}^{ {x}^{2} - {y}^{3} + 9 } \times ( - 3 {y}^{2} )$

$dz = Z'x \times dx + Z'y \times dy$

$dz = 2x {e}^{ {x}^{2} - {y}^{3} + 9 }dx - 3 {y}^{2} {e}^{ {x}^{2} - {y}^{3} + 9} dy \\ dz = {e}^{ {x}^{2} - {y}^{3} + 9 } (2xdx - 3 {y}^{2} dy)$