若f(x)是周期函数,则f'(x)必是周期函数?

问题描述:

若f(x)是周期函数,则f'(x)必是周期函数?

f(x+T)=f(x)
f'(x+T)=f'(x)
f'(x)为周期函数,周期也为T.能详细点吗 没理解f(x)是可导函数,则f(x+T)=f(x)两边对x求导得f'(x+T)*(x+T)'=f'(x)f'(x+T)=f'(x),周期为T.