Assuming that the equation F(x, y)=0 can determine the function y=y(x), then both sides of the equation take the derivative of x:

F/？ x+(？ F/？ y)(dy/dx)=0

So dy/dx=- (? F/？ x)/(？ F/？ y)；

For example, the equation F(x, y)= xy is known. +xe y+3x+siny = 0 can get the function y = y (x);

Another solution: take the derivative of x on both sides of the equation and get:

y？ +3xy？ y'+e^y+x(e^y)y'+3+(cosy)y'=0

(3xy？ +xe^y+cosy)y'=-(y？ +e^y+3)

∴y'=-(y？ +e^y+3)/(3xy？ +xe^y+cosy)

When using this method, remember: y? , e y, cosy are all functions of y, and y is a function of x, so when they are derived from x,

The chain derivative rule of compound function should be adopted; Namely d(xy? )/dx=？ (xy？ )/? x=[y？ +x(？ y？ /? y)(？ y/？ x)]=y？ +3xy？ y’；

The others are similar.