Find dydx, if y = [log(log(logx))]2 - Mathematics and Statistics

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Sum

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)))`

Concept: The Concept of Derivative - Derivatives of Logarithmic Functions
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Chapter 1.3: Differentiation - Q.4

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