好吧问答库 > x=g(y)是f(x)=lnx+arctanx的反函数求g✀(π⼀4)

x=g(y)是f(x)=lnx+arctanx的反函数求g✀(π⼀4)

过程详细，求教大神
2025年03月15日 02:50
有2个网友回答
网友（1）：

x=g(y)是f(x)=lnx+arctanx的反函数求g'(π/4)
解：∵ x=g(y)是f(x)=lnx+arctanx的反函数；
∴ g'(y)=1/f'(x)=1/[(1/x)+1/(1+x²)]=x(1+x²)/(x²+x+1).........①
x=1时，y=f(1)=ln1+arctan1=0+π/4=π/4; 将x=1代入①式即得：g'(π/4)=2/3;

网友（2）：

g'(π/4)=1/f'(π/4)
f'(x)=1/x+1/(x²+1)

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