Question

若f(x)=sinx,则它的导数f'(x)=cosx,这个导数怎么推出来的?

Answer 1

f'(x) = lim(h→0)[f(x+h)-f(x)]/h

= lim(h→0)[sin(x+h)-sinx]/h

= lim(h→0)2[sin(h/2)]cos(x+h/2)/h

= lim(h→0)cos(x+h/2)*lim(h→0)[sin(h/2)/(h/2)]

= cosx