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Miraj Kayastha

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- Thread starter Miraj Kayastha
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- #1

Miraj Kayastha

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- #2

Mark44

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No. If a function isn't defined on some interval, its derivative isn't defined there, either. The real function ln(x) is defined only for x > 0, as you are aware, so the domain for the derivative is x > 0, as well.

As it turns out, the function y = 1/x is defined for any ##x \ne 0##, but the left-hand branch does not represent the derivative of the natural log function.

- #3

lightarrow

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I assume you are referring to real numbers (you use "x" for the ind. variable and you say that lnx is defined for positive x only) because in the complex field it's all another story...

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lightarrow

- #4

mathman

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- #5

Svein

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In fact, [itex]\frac{d}{dx}ln(\lvert x \rvert)=\frac{1}{x} [/itex].

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