Question

найти du и d^2u для функции u=f(x;y)

Answer 1

$u=2x^4y-y^2\\u'_{x}=2ycdot 4x^3; ; ,; ; u'_{y}=2x^4-2y\\du=8x^3y, dx+(2x^4-2y)dy\\u''_{xx}=8ycdot 3x^2; ; ,; ; u''_{xy}=8x^3; ; ,; ; u'_{yy}=-2\\d^2u=24x^2ycdot dx^2+16x^3cdot dx, dy-2cdot dy^2$