复合导数y=lnsin1/xcos1/x / sin1/x=cot1/x吗

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复合导数y=lnsin1/xcos1/x/sin1/x=cot1/x吗复合导数y=lnsin1/xcos1/x/sin1/x=cot1/x吗复合导数y=lnsin1/xcos1/x/sin1/x=co

复合导数y=lnsin1/xcos1/x / sin1/x=cot1/x吗
复合导数
y=lnsin1/x
cos1/x / sin1/x=cot1/x吗

复合导数y=lnsin1/xcos1/x / sin1/x=cot1/x吗
设1/x=u,sinu=v,则y=lnv,
y'=1/v,
v'=cosu,
u'=-1/x,
y'=1/sin(1/x)*cos(1/x)*(-1/x^2).

补充:【1/sin(1/x)】*cos(1/x),即cos(1/x)/sin(1/x)=cot(1/x)

复合导数
y′=(1/sin1/x)*(cos1/x)*(-1/x^2)
==(cos1/x1/sin1/x)*(-1/x^2)
==cot(1/x1)*(-1/x^2)
==-cot(1/x1)/x^2