作业帮数学公式求推导、函数的和差积商的导数公式推导、只求商和积公式推导、在线等、
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/04/25 21:15:58
数学公式求推导、
函数的和差积商的导数公式推导、只求商和积公式推导、在线等、
函数的和差积商的导数公式推导、只求商和积公式推导、在线等、
(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'
(u/v)'=[u*v^(-1)]'
=u'*[v^(-1)]+[v^(-1)]'*u
=u'*[v^(-1)]+(-1)v^(-2)*v'*u
=u'/v - u*v'/v²
通分得
(u/v)=(u'v-uv')/v²
累死我了,请加分!
=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'
(u/v)'=[u*v^(-1)]'
=u'*[v^(-1)]+[v^(-1)]'*u
=u'*[v^(-1)]+(-1)v^(-2)*v'*u
=u'/v - u*v'/v²
通分得
(u/v)=(u'v-uv')/v²
累死我了,请加分!