商的导数公式的推导过程.(u/v)=(u'v-uv')/v²要高中生能看得懂的...

首先说积的导数是UV=U'V+VU;
那么商:U/V=U(1/V)=U'(1/V)+U(1/V)'=U'/V-U(V'/V²)=(U'V-UV')/V²

(u/v)'=[u*v^(-1)]'
=u' * [v^(-1)] +[v^(-1)]' * u
= u' * [v^(-1)] + (-1)v^(-2)*v' * u
=u'/v - u*v'/(v^2)
通分,易得
(u/v)=(u'v-uv')/v²