arctane^x arctane^(-X)

函数y=arctane^x求dyy'=e^x/(1+e^2x)dy=e^xdx/(1+e^2x)函数y=y(x)由方程x-y-e^y=0确定,求y'(0)两边对x求导：1-y'-y'e^y=0y'=1

公式推导：设arctanA=a,arctan(1/A)=b则tana=A,tanb=1/A,即tana*tanb=1那么sinasinb=cosacosb所以cos(a+b)=0,a+b=π/2既然有

y=2xarctan(y/x)(y/x)'=(y'/x-y/x^2)(arctanu)'=1/(1+u^2)y'=2arctan(y/x)+2x*(y'/x-y/x^2)*[1/(1+(y/x)^2)