用定义求一下导数
lim x->0 [F(x)-F(0)]/(x-0)
=lim x->0 f(x)(1+|sinx|)/x
=lim x->0 f(x)/x
=lim x->0 [f(x)-f(0)]/(x-0)
=f'(0)
所以F(X)=f(x)(1+/SINX/)在x=0处可导
用定义求一下导数
lim x->0 [F(x)-F(0)]/(x-0)
=lim x->0 f(x)(1+|sinx|)/x
=lim x->0 f(x)/x
=lim x->0 [f(x)-f(0)]/(x-0)
=f'(0)
所以F(X)=f(x)(1+/SINX/)在x=0处可导