sinxy=xy求dy

Question

sinxy =xy 求dy

Answer 1

sin(xy) =xy
典型的隐函数求导,两边对x求导即可：
cos(xy)*(y+x*dy/dx)=y+x*dy/dx
展开
cos(xy)*y+cos(xy)*x*dy/dx=y+x*dy/dx
两边乘以dx
cos(xy)*y*dx+cos(xy)*x*dy=y*dx+x*dy
移项
cos(xy)*y*dx-y*dx=x*dy-cos(xy)*x*dy
dy=[cos(xy)*y*dx-y*dx]/[x-cos(xy)*x]