Question

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,

Answer 1

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