设z=uv,u=e^(x+y),v=ln(xy)求dy
问题描述：
设z=uv,u=e^(x+y),v=ln(xy)求dy
答
dy/dx=dy/du *du/dx+dy/dv*dv/dx
=v*e^(x+y)+u*y/x
=ln(xy) *e^(x+y)+e^(x+y)*y/x
=e^(x+y)[ln(xy)+y/x]
所以dy=e^(x+y)[ln(xy)+y/x]dx