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Question
Differentiate the following w.r.t.x: [log {log(logx)}]2
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Solution
Let y = [log {log(logx)}]2
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[log{log(logx)}]^2`
= `2.log{log(logx)} xx "d"/"dx"[log{log(logx)}]`
= `2.log{log(logx)} xx (1)/(log(logx))."d"/"dx"[log(logx)]`
= `2.log{log(logx)} xx (1)/(log(logx)). (1)/(logx) xx "d"/"dx"(logx)`
= `2.log{log(logx)} xx (1)/(log(logx)). (1)/(logx) xx (1)/x`
= `2.[(log{log(logx)})/(x.logx.log(logx))]`.
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