求导数或微分1.y=sinx-cosx,求y'|x=π/62.y平方-2xy+9=0,求dy/dx3.y=xsin2x,求dy
问题描述：
求导数或微分
1.y=sinx-cosx,求y'|x=π/6
2.y平方-2xy+9=0,求dy/dx
3.y=xsin2x,求dy
答
y'=cosx+sinx
y'|x=π/6 = 1/2+(根号3)/3
y^2-2xy+9=0
y看成x的函数,2边对x求导有
2y*dy/dx-2y-2x*dy/dx=0
dy/dx=y/(y-x)
dy=(sin2x+2xcos2x)dx
答
1. y=sinx-cosx,求y'|x=π/6
y'=cosx + sinx
y'|x=π/6 = (√3)/2 + 1/2
2. y^2 -2xy+9=0,求dy/dx
直接对方程求关于x的导数：2y* y' - 2（y + xy')=0
整理,得 y' = y/(y-x)
3. y=xsin2x,求dy
y' = sin2x + 2xcos2x
dy = y' dx = (sin2x + 2xcos2x)dx