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Find the Nth Derivative of Cos 5x.Cos 3x.Cos X. - Applied Mathematics 1

Find the nth derivative of cos 5x.cos 3x.cos x. 

 

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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, 

𝒏 𝒕𝒉 π’…π’†π’“π’Šπ’—π’‚π’•π’Šπ’—π’† 𝒐𝒇 𝒄𝒐𝒔 `(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)`

Concept: Review of Complex Numbers‐Algebra of Complex Number
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