`F(s) = ln ln s` Differentiate the function.

Textbook Question

Chapter 3, 3.6 - Problem 15 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to differentiate the function with respect to variable s, using the chain rule, such that:

`F'(s) = (ln ln s)'`

`F'(s) = ln'(ln s)*(ln s)'*(s)'`

`F'(s) = 1/(ln s)*(1/s)*1`

`F'(s) = 1/(s*ln s)`

Using the power property of logarithms, yields:

`F'(s) = 1/(ln s^s)`

Hence, evaluating the derivative of the given function, yields `F'(s) = 1/(ln s^s).`

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