设y=y(x)是由方程cos(xy)=x 确定的隐函数,则dy是?怎么解的_数学解答

设y=y(x)是由方程cos(xy)=x 确定的隐函数,则dy是?怎么解的

人气：350 ℃　时间：2019-08-18 12:52:52

解答

dcos(xy)=dx
-sin(xy)d(xy)=dx
-sin(xy)(ydx+xdy)=dx
-ysin(xy)dx-xsin(xy)dy=dx
dy=-[ysin(xy)+1]dx/[xsin(xy)]