導(dǎo)數(shù)的乘法法則推倒
uv)'=lim(h→0)[u(x+h)v(x+h)-uv]/h
=lim(h→0)[u(x+h)v(x+h)+u(x+h)v-u(x+h)v-uv]/h
=lim(h→0)[u(x+h)]×[v(x+h)-v(x)]/h+lim(h→0)[v(x)]×[u(x+h)-u(x)]/h
=u(x)v'(x)+u'(x)v(x)
=u'v+uv'請問這個第一步lim(h→0)[u(x+h)v(x+h)-uv]/h 是怎么來的
我算出來的的第一步是
[u(x+h)-u(x)]/h*[v(x+h)-v(x)]/h
=u(x+h)v(x+h)-u(x+h)v(x)-u(x)v(x+h)+u(x)v(x)/h*h
然后呢 因?yàn)閔->0就消掉么?