find the nth differential coefficient of cosx cos2x cos3x
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Step-by-step explanation:
We have
y=cosx⋅cos2x⋅cos3x
∴y=12⋅cosx⋅2cos2x⋅cos3x=12⋅cosx⋅[cos5x+cosx]
∴y=12⋅cosx⋅cos5x+15⋅cosx⋅cosx
∴y=14[cos6x+cos4x+1+cos2x]
Usign formula,
y=cos(ax+b) then yn=ancos(ax+b+nπ2)
∴yn=14[6ncos(6x+nπ2)+4ncos(4x+nπ2)+2ncos(2x+nπ2))
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