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Question
Find the nth derivative of cos 5x.cos 3x.cos x.
Solution
let y =` cos 5x.cos 3x.cos x`
= `(cos(5x-3x)+cos(5x+3x))/2. cos x`
=`1/2[cos 2x.cos x+cos x+cos8x.cos x]`
`y =1/4[cos 3x+cos x +cos 9x +cos 7x]`
Take n th derivative,
๐ ๐๐ ๐ ๐๐๐๐๐๐๐๐๐ ๐๐ ๐๐๐ `(ax+b)=a^n cos ((npi)/2+ax+b)`
`y_n=1/4[9cos((npi)/2+3x)+cos((npi)/2+x)+81cos((npi)/2+9x)+49cos((npi)/2+7x)`
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