f(x)=cosx,f'(x)=?

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f(x)=cosx,f'(x)=?

f(x)=cosx,f'(x)=?
f(x)=cosx,f'(x)=?

f(x)=cosx,f'(x)=?
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
这样可以么?

f'(x)=(cosx)'=-sinx