设方程x小3 y小2+2xy+3x+5y+1=0确定y为x的隐函数求dx分之dy

设方程x小3 y小2+2xy+3x+5y+1=0确定y为x的隐函数求dx分之dy

令f=x^3+y^2+2xy+3x+5y+1
则df=3x^2dx+2ydy+2xdy+2ydx+3dx+5dy=0
即(3x^2+2x+3)dx+(2y+2x+5)dy=0
于上dy/dx=-(3x^2+2x+3)/(2y+2x+5)