Question

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

 

Answer 1

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 𝒅𝒆𝒓𝒊𝒗𝒂𝒕𝒊𝒗𝒆 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)`