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

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/06 05:06:38
f(x)=cosx,f'(x)=?
x)KӨдM/IS1mT b+*djd

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