Найти полный дифференциал: y=y^2/3x arcsinxy

dz = dz/dx * dx + dz/dy * dy

dz/dx = ((x - y) ^3 + x^ (1/2) * sin y^2 + x * y) '_x =

= 3 * (x - y) ^2 + 1/2 * x^ (-1/2) * sin y^2 + y

dz/dy = ((x - y) ^3 + x^ (1/2) * sin y^2 + x * y) '_y =

= - 3 * (x - y) ^2 + x^ (1/2) * cos y^2 * 2y + x

Тогда

dz = (3 * (x - y) ^2 + 1/2 * x^ (-1/2) * sin y^2 + y) dx +

+ (-3 * (x - y) ^2 + 2 * x^ (1/2) * y * cos y^2 + x) dy