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Question
Find `("d"y)/("d"x)`, if y = [log(log(logx))]2
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Solution
y = [log(log(logx))]2
Differentiating both sides w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x)[log(log(logx))]^2`
= `2[log(log(logx))] xx "d"/("d"x)[log(log(logx))]`
= `2[log(log(logx))] xx 1/(log(logx)) xx "d"/("d"x)[log(logx)]`
= `2[log(log(logx))] xx 1/(log(logx)) xx 1/logx xx "d"/("d"x)(log x)`
= `2[log(log(logx))] xx 1/(log(logx)) xx 1/logx xx 1/x`
∴ `("d"y)/("d"x) = (2[log(log(logx))])/(x(logx)(log(logx)))`
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