(uv)'=lim[u(x+h)v(x+h)-uv]/h

　　=lim[u(x+h)v(x+h)+u(x+h)v-u(x+h)v-uv]/h

　　=limu(x+h)[v(x+h)-v(x)]/h+limv(x)[u(x+h)-u(x)]/h

　　=u(x)v'(x)+u'(x)v(x)

　　=u'v+uv'h→0