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Question
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
Options
`(-y^2tanx)/(1 - ylog cosx)`
`(-y^2tanx)/(1 + ylog cosx)`
`(ytanx)/(1 - ylog cosx)`
`(ytanx)/(1 + ylog cosx)`
MCQ
Fill in the Blanks
Solution
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = `(-y^2tanx)/(1 - ylog cosx)`.
Explanation:
If y = `"f"(x)^("f"(x)^("f"(x)^(...oo)`, then `("d"y)/("d"x) = (y^2"f'"(x))/("f"(x)[1 - ylog"f"(x)]`
∴ `("d"y)/("d"x) = (-y^2sinx)/(cosx(1 - ylog cosx))`
= `(-y^2tanx)/(1 - ylog cosx)`
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