求方程所确定的隐函数的导数dy/dx?
问题描述:
求方程所确定的隐函数的导数dy/dx?
x^3+y^3-3x^2*y=0
答
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)