已知ysinx-cos(x+y)=0,求在点(0,π/2)的dy/dx值
问题描述：
已知ysinx-cos(x+y)=0,求在点(0,π/2)的dy/dx值
答
ysinx-cos(x+y)=0,两边对x求导,得
y'sinx+ycosx+(1+y')sin(x+y)=0,解得
y'=-[ycosx+sin(x+y)]/[sinx+sin(x+y)]
dy/dx=y'(0,π/2)=-(π/2+1)/(0+1)=-(π/2+1)