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2^(cos^(2)) x...

`2^(cos^(2)) x`

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Let ` y = 2^(cos^(2))x`
` :. log y = log2^(cos^(2)x) = cos^(2).log2`
On differentiating w.r.t x, we get
`d/(dy) log y. (dy)/(dx) = (d)/(dx)log2. cos^(2)x`
`rArr 1/y. (dy)/(dx) = log 2 d/(dx) (cosx)^(2)`
`rArr 1/y.(dy)/(dx) = log2.[2cosx].(d)/(dx) cosx`
` = log2.2 cos x. (-sinx)`
`= log2.[-(sin2x)]`
`:. (dy)/(dx) = - y .log2 (sin2x)`
` = - 2^(cos^(2))x. log2(sin2x)`
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