Question

由方程 x^2y^3+4x^2y^2-9=0确定y是x的隐函数,求 =y'?

Answer 1

两边对x求导：

2xy^3+x^2*3y^2*y'+8xy^2+8x^2y*y'=0

得：y'=-(2xy^3+8xy^2)/(3x^2y^2+8x^2y)=-2xy^2(y+4)/[x^2y(3y+8)]=-2y(y+4)/[x(3y+8)]