Y=sinX．cos3X的二阶导数是多少？
做到这么复杂,不如试下化简吧!y=sinx·cos3x
一阶导数dy/dx=cos3x·d(sinx)/dx+sinx·d(cos3x)/d(3x)·d(3x)/dx
=cos3x·cosx+sinx·(-sin3x)·3
=cosxcos3x-3sinxsin3x,这是一阶导数的答案,开始化简
=cosxcos3x-sinxsin3x-2sinxsin3x,头2项组成倍角公式,最后1项是积化和差公式
=cos(x+3x)-2·(-1/2)[cos(x+3x)-cos(x-3x)]
=cos4x+cos4x-cos(-2x)
=2cos4x-cos2x
二阶导数d²/dx²=2·d[cos(4x)]/d(4x)·d(4x)/dx-d[cos(2x)]/d(2x)·d(2x)/dx
=2(-sin4x)·4-(-sin2x)·2
=2sin2x-8sin4x,这是二阶导数的答案
适当的括号是必须的，能给加括号吗？假设是下面这一种：
y
=
㏑√[(1+sinx)/(1-sinx)]，
改写成
y
=
(1/2)[㏑(1+sinx)-ln(1-sinx)]，
求导，得
y'
=
(1/2)[cosx/(1+sinx)+cosx/(1-sinx)]，
再求导，
y"
=
……
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