>>446>>422双曲関数に目が行くが
e^x=A
f=(A-(1/A))/(A+(1/A)^3, x>OとしてA>1
f^2=(A^2+(1/A^2)-2)/((A^2+(1/A^2)+2))^3, A^2+(1/A^2)=t
f^2=(t-2)/(t+2)^3
ln(f^2)=ln(t-2)-3*ln(t+2),
(ln(f^2))'=1/(t-2)-3/(t+2)=(8-2t)/(t-2)(t-2)=０
4=t=A^2+(1/A^2), A^2=2±√3,
Max^2=(4-2)/(4+2)^3=1/(3*2*3*2*3), Max=1/(6√3)