`(d^(20))/(dx^(20))(2cosxcos3x)=` `2^(20)(cos2x-2^(20)cos4x)` (b) `2^(20)(cos2x+2^(20)cos4x)` (c) `2^(20)(sin2x+2^(20)sin4x)` (d) `2^(20)(sin2x-2^(20)sin4x)`

Explanation

(b) `2^{20}(cos 2 x+2^{20} cos 4 x)`

Here,
`

y=2 cos x cos 3 x=cos (3 x-x)+cos (3 x+x) `
`
=cos 2 x+cos 4 x `
`
Rightarrow frac{d y}{d x}=-2 sin 2 x-4 sin 4 x=-2(sin 2 x+2 sin 4 x) `
`
Rightarrow frac{d^{2} y}{d x^{2}}=-4 cos 2 x-16 cos 4 x=-2^{2}(cos 2 x+2^{2} cos 4 x) `
`
Rightarrow frac{d^{3} y}{d x^{3}}=2^{3}(sin 2 x+2^{3} sin 4 x) `
`
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