Question

证明arshx的导数为1/(√1+x²)

Answer 1

y=arcshx,
x=shy=[e^y-e^(-y)]/2;
dx=[e^y+e^(-y)]dy/2
dy/dx=2/[e^y+e^(-y)]
而e^y+e^(-y)=√[e^(2y)+e^(-2y)+2] =√[4x^2+4]
故dy/dx=2/√[4^2+4]=1/√[1+x^2]