求导数乘法和除法法则的证明,

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