What is the domain of the derivative of #ln x#?

Answer 1
The domain of the derivative of #lnx# is #(0, oo)#.
The domain of #f'# is a subsest of the domain of #f#.
Because the domain of #lnx# is #(0, oo)#, the domain of its derivative which is defined to be: #lim_(hrarr0)(ln(x+h)-lnx)/h# cannot include any negative numbers.
Of course, we know that the derivative of #f(x) = ln(x)# is #f'(x) = 1/x#, which, as the derivative of #ln# has domain #(0, oo)#.
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Answer 2

The domain of the derivative of ln(x) is the set of all positive real numbers, excluding zero.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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