y=Insin(3x-1),求dx分之dy

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y=Insin(3x-1),求dx分之dy

y=Insin(3x-1),求dx分之dy
y=Insin(3x-1),求dx分之dy

y=Insin(3x-1),求dx分之dy
y=lnsin(3x-1)
  dy/dx=d【lnsin(3x-1)】/d【sin(3x-1)】×d【sin(3x-1)】/d(3x-1)×d(3x-1)/dx
  =1/sin(3x-1)×cos(3x-1)×3
  =3cot(3x-1)

y'=[Insin(3x-1)]'
=1/sin(3x-1)*[sin(3x-1)]'
=cos(3x-1)/sin(3x-1)*[(3x-1)]'
=3cot(3x-1)

设u=sin(3x-1)
则dy/dx=(dy/du)(du/dx)=(1/u)(du/dx)
设v=3x-1,则dv/dx=(3x-1)'=3
∴du/dx=(du/dv)(dv/dx)=3(cosv)=3cos(3x-1)
∴dy/dx=(1/u)(3cos(3x-1))=3cos(3x-1)/(sin(3x-1))=3cot(3x-1)
即:dy/dx=3cot(3x-1)
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y=lnsin(3x-1)
dy/dx=(lnsin(3x-1))'
=1/sin(3x-1) *(sin(3x-1))'
=1/sin(3x-1) *cos(3x-1)*(3x-1)'
=3cos(3x-1)/sin(3x-1)
=3ctan(3x-1)

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