如何推导简单公式?

问：如何推导简单公式?

来自山西省离石市的网友五河金枝的解答：

  呵呵。
   (1)f'(x)=(x→Δx)lim[(sinx-sinΔx)/(x-Δx)] ````````=(x→Δx)lim[2cos(x/2+Δx/2)sin(x/2-Δx/2)/(x→Δx)] ````````=(x→Δx)lim[2cos(x/2+Δx/2)sin(x/2-Δx/2)/(x/2-Δx/2)]*1/2 ````````=(x→Δx)lim[2cosx*1]*1/2 ````````=cosx (2)f'(x)=(x→Δx)lim[(cosx-cosΔx)/(x-Δx)] ````````=-(x→Δx)lim[2sin(x/2+Δx/2)sin(x/2-Δx/2)/(x-Δx)] ````````=-(x→Δx)lim[2sinxsin[(x-Δx)/2]/[(x-Δx)/2]]*1/2 ````````=-(x→Δx)lim[2sinx*1/2] ````````=-sinx。