(ax+b)sinx find nth derivative
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let y=(ax+b)sinx
dy/dx=d/dx(axsinx)+d/dxbsinx
=axcosx+asinx+bcosx=(ax+b)cosx+asinx
d²y/dx²=-(ax+b)sinx+acosx+acosx
=-(ax+b)sinx+2acosx
d³y/dx³=-(ax+b)cosx-asinx-2asinx
=-(ax+b)cosx-3asinx
d⁴y/dx⁴=(ax+b)sinx-acosx-3acosx
=(ax+b)sinx-4acosx
hence d^n/dx^n=±(ax+b)sinx±nacosx
or=±(ax+b)cosx±nsinx
dy/dx=d/dx(axsinx)+d/dxbsinx
=axcosx+asinx+bcosx=(ax+b)cosx+asinx
d²y/dx²=-(ax+b)sinx+acosx+acosx
=-(ax+b)sinx+2acosx
d³y/dx³=-(ax+b)cosx-asinx-2asinx
=-(ax+b)cosx-3asinx
d⁴y/dx⁴=(ax+b)sinx-acosx-3acosx
=(ax+b)sinx-4acosx
hence d^n/dx^n=±(ax+b)sinx±nacosx
or=±(ax+b)cosx±nsinx
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