Question

隐函数x^3-3xy^2+y^3=1,则当x=2,y=-1时,y'=()

Answer 1

x^3-3xy^2+y^3=1

两边对x求导,

d(x^3-3xy^2+y^3)/dx=d1/dx

d(x^3)/dx-3xd(y^2)/dx-y^2d(3x)/dx+d(y^3)/dx=0

2x^2-6xydy/dx-3y^2+3y^2dy/dx=0

将x=2,y=-1代入,

8+12dy/dx-3+3dy/dx=0

dy/dx=-1/3

即y'=-1/3