2x²y-xy²+y³=0方程所确定的隐函数y的导数dy/dx

2x²y-xy²+y³=0方程所确定的隐函数y的导数dy/dx
2x²y-xy²+y³=0方程所确定的隐函数y的导数dy/dx

2x²y-xy²+y³=0方程所确定的隐函数y的导数dy/dx
∵2x²y-xy²+y³=0 ==>4xydx+2x²dy-y²dx-2xydy+3y²dy=0
==>(4xy-y²)dx=(2xy-2x²-3y²)dy
∴dy/dx=(4xy-y²)/(2xy-2x²-3y²).