這個非?；镜膯栴},如果要是從0開始學的話,要講好幾堂課的.所以
首先具備極限知識的基礎：當 x → 0 時,lim sinx /x = 1
其次導數(shù)的定義：f'(x) = lim [f(x+Δx) - f(x)]/Δx 當 Δx → 0 時的極限.
(cosx)' = Δx→0 lim [cos(x+Δx) - cosx]/Δx
其中
cos(x+Δx) - cosx
= cos[x + Δx/2 + Δx/2] - cos(x + Δx/2 - Δx/2]
= cos(x+ Δx/2)cos(Δx/2) - sin(x+ Δx/2)sin(Δx/2) - cos(x+ Δx/2)cos(Δx/2) - sin(x + Δx/2)sin(Δx/2)
= -2 sin(x + Δx/2)sin(Δx/2)
(cosx)' = Δx→0 lim -2 sin(x +Δx/2)sin(Δx/2) /Δx
= Δx→0 lim - sin(x + Δx/2) [sin(Δx/2)/(Δx/2)]
= Δx→0 lim - sin(x + Δx/2)
= - sinx