`f(x) = ln(1/x)` Differentiate the function.

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Textbook Question

Chapter 3, 3.6 - Problem 5 - 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 x, using the chain rule, such that:

`f'(x) = (ln(1/x))'`

`f'(x) = (ln'(1/x))*(1/x)'`

`f'(x) = (1/(1/x))*(-1/(x^2))`

`f'(x) = -x/(x^2)`

Reducing like terms, yields:

`f'(x) = -1/x`

Hence, evaluating the derivative of the given function, yields `f'(x) = -1/x.`

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