Question

求方程所确定的隐函数的导数dy/dx?

x^3+y^3-3x^2*y=0

Answer 1

x^3+y^3-3x^2*y=0
对x求导
3x^2+3y^2*y'-(6xy+3x^2y')=0
3x^2-6xy+(3y^2-3x^2)y'=0
y'=(2xy-x^2)/(y^2-x^2)
所以dy/dx=(2xy-x^2)/(y^2-x^2)

Answer 2

对上式求关于X的导数(y是x函数)
3x^2+3y^2*y'-(6xy+3x^2*y')=0
x^2+y^2*y'-(2xy+x^2*y')=0
y'(y^2-x^2)=2xy-x^2
y'=(2xy-x^2)/(y^2-x^2)
dy/dx=y'=(2xy-x^2)/(y^2-x^2)

Answer 3

两边求导
3x^2+3y^2*y'-6x*2y-3x^2*2y'=0
y'(3y^2-6x^2)=12xy-3x^2

dy/dx=y'=(12xy-3x^2)/(3y^2-6x^2)