df(x)/dx=lim{[f(x+Δx)-f(x)]/Δx}=lim{[sin(x+Δx)-sinx]/Δx}
=lim{[2cos(x+Δx/2)sin(Δx/2)]/Δx}=lim{cos(x+Δx/2)[sin(Δx/2)/(Δx/2)]}
=cosx such that Δx→0