求由方程ysinx-cos(xy)=0所确定的隐函数y=y(x)的导数dy/dx

题目

求由方程ysinx-cos(xy)=0所确定的隐函数y=y(x)的导数dy/dx

答案

ysinx=cos(xy)
两边分别求导
y'sinx+ycosx=-sin(xy)(y+xy')
y'=-y(sin(xy)+cosx)/(sinx+xsin(xy))