导数运算时有加减乘除是先算导数还是先

Question

如题所述

Answer 1

复合函数的求导
y=u/v，y'=(u'v-uv')/v²
y=uv，y'=u'v+uv'
y=u+v，y'=u'+v'
y=u-v，y'=u'-v'
y=sinx-x*sinx/cosx-x*sinx
y'=(sinx)'-(x*sinx/cosx)'-(x*sinx)'=cosx-(x'*sinx/cosx+x*(sinx/cosx)')-(x'sinx+x*(sinx)')
=cosx-(sinx/cosx+x*[(sinx)'cosx-sinx(cosx)']/(cosx)²)-(sinx+x*cosx)
=cosx-(sinx/cosx+x*(cos²x+sin²x)/(cosx)²)-(sinx+x*cosx)
=cosx-sinx/cosx-x/cos²x-sinx-x*cosx
=cosx-sinx
-x*cosx
-sinx/cosx
-
x/cos²x
口算，可能有错误，自行验算。