方程arctan(y/x)=ln√(x²+y²)两边对x求导
问题描述：
方程arctan(y/x)=ln√(x²+y²)两边对x求导
答
arctan(y/x)=1/2*ln(x^2+y^2)两边对x求导：1/(1+y^2/x^2)* (y/x)'=1/2*1/(x^2+y^2)*(x^2+y^2)'x^2/(x^2+y^2)* (xy'-y)/x^2=1/(x^2+y^2)*(x+yy')xy'-y=x+yy'y'=(x+y)/(x-y)