Question

28 БАЛЛОВ СРОЧНО! Решить задание на фото! Пожалуйста!

Answer 1

$\displaystile1)\frac{\partial u}{\partial x}=6*2x+0+2y*3x^2+0-0=12x+6x^2y\\\\\frac{\partial^2 u}{\partial x^2}=12+6y*2x=12x+12xy\\\\2)\frac{\partial u}{\partial y}=0+3*2y+2x^3-5-0=2x^3+6y-5\\\\\frac{\partial^2 u}{\partial y^2}=0+6-0=6\\\\3)\frac{\partial^2 u}{\partial x \partial y}=(6x^2y+12x)'_y=6x^2+0=6x^2$

Answer 2

$u=6x^2+3y^2+2x^3y-5y-11\\\\u'_x}=12x+6x^2y\\\\u'_{y}=6y+2x^3-5\\\\u''_{xx}=12+12xy\\\\u''_{xy}=6x^2=u'_{yx}\\\\u''_{yy}=6$