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Differentiate log[log(logx^(5))]...

Differentiate `log[log(logx^(5))]`

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The correct Answer is:
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Let `y = log[log(logx^(5))]`
`:. (dy)/(dx) = (d)/(dx) [log(loglogx^(5))]`
`= (1)/(loglogx^(5)).(d)/(dx)(log.logx^(5))`
`=(1)/(loglogx^(5)).(1/(logx^(5))).(d)/(dx) logx^(5)`
`= (1)/(loglogx^(5)).(1)/(logx^(5)).(d)/(dx) (5logx)= (5)/(x.log(logx^(5)).log(x^(5)))`
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