设函数u(x,y)=q(x+y)+q(x-y)+定积分(x-y)到(x+y)p(t)dt,其中函数q具有二阶导数,p具有一阶导数,则必有A.x的二阶偏导数=负的y的二阶偏导数B.x的二阶偏导数=y的二阶偏导数C二阶混合偏导数=y的二阶偏导数

Question

设函数u(x,y)=q(x+y)+q(x-y)+定积分(x-y)到(x+y)p(t)dt,其中函数q具有二阶导数,p具有一阶导数,则必有
A.x的二阶偏导数=负的y的二阶偏导数B.x的二阶偏导数=y的二阶偏导数C二阶混合偏导数=y的二阶偏导数D二阶混合偏导数=X的二阶偏导数

Answer 1

u(x,y)=q(x+y)+q(x-y)+∫(x-y)到(x+y)p(t)dt
u'x=q'(x+y)+q'(x-y)+p(x+y)-p(x-y)
u'y=q'(x+y)-q'(x-y)+p(x+y)+p(x-y)
u''xx=q''(x+y)+q''(x-y)+p'(x+y)-p'(x-y)
u''yy=q''(x+y)+q'’(x-y)+p'(x+y)-p'(x-y)
选B.x的二阶偏导数=y的二阶偏导数