Question

求u=sin(x²-y2z)的全微分

Answer 1

全微分就是对xyz分别求偏导
再一起写成微分相加即可
这里的u=sin(x²-y+2z)
那么u'x=2x *cos(x²-y+2z)，u'y= -cos(x²-y+2z)
u'z=2cos(x²-y+2z)
于是全微分dz=2x *cos(x²-y+2z)dx -cos(x²-y+2z)dy +2cos(x²-y+2z)dz

Answer 2

u=sin(x²-y+2z)
du=u'xdx+u'ydy+u'zdz
u'x=2x *cos(x²-y+2z)
u'y= -cos(x²-y+2z)
u'z=2cos(x²-y+2z)
du=cos(x²-y+2z)(2xdx -dy +2dz)