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Question
`log [log(logx^5)]`
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Solution
Let y = `log [log(logx^5)]`
Differentiating both sides w.r.t. x
`"dy"/"dx" = "d"/"dx" log [log(log x^5)]`
= `1/(log(log x^5)) xx "d"/"dx" log (log x^5)`
= `1/(log(log x^5)) xx 1/(log(x^5)) xx "d"/"dx" log x^5`
= `1/(log(log x^5)) * 1/(log (x^5)) * 1/x^5 * "d"/"dx" x^5`
= `1/(log(log x^5)) * 1/(log(x^5)) * 1/x^5 * 5x^4`
= `5/(x log (x^5) * log (log x^5))`
Hence, `"dy"/"dx" = 5/(x log (x^5) * log (log x^5))`
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