令F(x,y)=ln根号(x^2+y^2)-arctan(y/x)
对F(x,y)求x的偏册迹导数Fx=(x + y)/(x^2 + y^2)
对F(x,y)求y的偏坦姿搭导数Fy=-(x - y)/(x^2 + y^2)
根据隐函数求导公式可得:
y'=-Fx/Fy
=(x + y)/让拿(x - y)
(1/2)ln(x^2+y^2)=arcy/x
同时求导数
[2x+2y*y']/[2(x^2+y^2)]=(y'搏春x-y)/[x^2(1+y^2/基迟耐x^2)]
化旦歼简2x^3(1+y^2/x^2)+2yy'(x^2(1+y^2/x^2)=2(x^2+y^2)(y'x-y)
2x^3+2xy^2+2yy'x^2+2y^3y'=2x^2y'x+2y^2y'x-2x^2y-y^3