Question

u=x sin xy+y cos xy. Найти d^2/dx^2

Answer 1

$u=xcdot sinxy+ycdot cosxy\\frac{partial u}{partial x}=sinxy+xcdot cosxycdot y+ycdot (-sinxy)cdot y=\\=sinxy+xycdot cosxy-y^2cdot sinxy=(1-y^2)cdot sinxy+xycdot cosxy\\frac{partial ^2u}{partial x^2}=(1-y^2)cdot cosxycdot y+ycdot cosxy+xycdot (-sinxy)cdot y=\\=(1-y^2)cdot ycdot cosxy+ycdot cosxy-xy^2cdot sinxy=\\=(2-y^2)cdot ycdot cosxy-xy^2cdot sinxy$