Question

найти du и d^2u для функции u=f(x;y)

Answer 1

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