Question

设y为x的函数是由方程ln根号（x平方加y平方）＝arctan y/x 确定的,求y'

Answer 1

令F(x,y)=ln根号(x^2+y^2)-arctan(y/x)
对F(x,y)求x的偏导数Fx=(x + y)/(x^2 + y^2)
对F(x,y)求y的偏导数Fy=-(x - y)/(x^2 + y^2)
根据隐函数求导公式可得：
y'=-Fx/Fy
=(x + y)/(x - y)