Предмет: Алгебра, автор: adina2302

Найти полные дифференциалы данной функции
$z=5xy^2-3x^3y^4$

Ответы

Автор ответа: Аноним

Найдем частные производные.
Частная производная по $x$ , считаем аргумент $y-const$
$dfrac{partial z}{partial x} =5y^2-9x^2y^4$

Частная производная по $y$ , считаем аргумент $x-const$
$dfrac{partial z}{partial y} =10xy-12x^3y^3$

Полный дифференциал функции:
$dz= dfrac{partial z}{partial x} dx+ dfrac{partial z}{partial y} dy$

$dz=(5y^2-9x^2y^4)dx+(10xy-12x^3y^3)dy$

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