Question

求函数fx=sinx导数的过程

Answer 1

Δy=sin(x+Δx)-sinx=2cos(x+Δx/2)sin(Δx/2)

Δy/Δx=cos(x+Δx/2)sin(Δx/2)/(Δx/2)

(sinx)‘=lim(Δx-->0)cos(x+Δx/2)sin(Δx/2)/(Δx/2)

=lin(Δx/2-->0)cos(x+Δx/2)sin(Δx/2)/(Δx/2)

=(cosx)*lim(Δx/2-->0sin(Δx/2)/(Δx/2)

=(cosx)*1=cosx