dy/dx=n{x+√(x2-1)}n-1(1+x/√(x2-1)).
Let u=n{x+√(x2-1)}n-1 and v=1+x/√(x2-1).
du/dx=n(n-1)n{x+√(x2-1)}n-2(1+x/√(x2-1));
dv/dx=(√(x2-1)-x2/√(x2-1))/(1+x/√(x2-1))2=
-1/(√(x2-1)(1+2x/√(x2-1)+x2/(x2-1))=
-1/(√(x2-1)+2x+x2/√(x2-1))=-√(x2-1)/(2x2+2x√(x2-1)-1).
dy/dx=uv, d2y/dx2=v(du/dx)+u(dv/dx)=
(1+x/√(x2-1))(n(n-1)n{x+√(x2-1)}n-2(1+x/√(x2-1)))+
-(n{x+√(x2-1)}n-1)(√(x2-1)/(2x2+2x√(x2-1)-1)).