Question

求下列由方程所确定的隐函数y=y(x)的导数dy/dx e^x-e^y-sinxy=0

Answer 1

答：
e^x-e^y-sin(xy)=0
两边对x求导：
e^x -(e^y)y'-cos(xy)*(y+xy')=0
所以：
[xcos(xy)+e^y]*y'=e^x-ycos(xy)
所以：
dy/dx=y'= [e^x-ycos(xy) ] / [ xcos(xy)+e^y ]