Question

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、

Answer 1

(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!