因为f(x)在x=a可导,所以
f(a+nh)=f(a)+f'(a)nh+o(nh),
f(a-mh)=f(a)-f'(a)mh+o(mh),
f(a+nh)-f(a-mh)=f'(a)(m+n)h+o(h)
所以lim(f(a+nh)-f(a-mh))/h=(m+n)f'(a)