① lim [(x+1)/(x-1)]^(x+2) = lim [1+2/(x-1)]^(x+2)
= lim { [1+2/(x-1)]^[(x-2)/2] }^[2(x+2)/(x-2)] =e^2.
② lim(x→0) [(1/sinx)-(1/x)] = lim(x→0) (x-sinx)/(xsinx)
= lim(x→0) (x-sinx)/x^2 = lim(x→0) (1-cosx)/(2x)
= lim(x→0) (x^2/2)/(2x) = 0.
(1) y=lncos6x,y'=(1/cos6x)(-sin6x)*6 = -6tan6x.
(2) y=ln[√(x^2+1)+x],
y'={1/[√(x^2+1)+x]}*[x/√(x^2+1)+1] = 1/√(x^2+1),
y''= -(1/2)[1/(x^2+1)^(3/2)](2x) = -x/(x^2+1)^(3/2)].