On what interval is the function #ln((4x^2)+9)# differentiable?

Answer 1

In all the Real Field.

A function can be differentiable in its Domain.

The Domain of this function can be found solving this inequality:

#4x^2+9>0#
The solution is #AAx#, so it is always differentiable.
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Answer 2

The function ln((4x^2)+9) is differentiable for all real numbers x except at the points where the function is not defined or where its derivative does not exist. Since ln((4x^2)+9) is defined for all real numbers, it is differentiable on the entire real number line, which means it is differentiable on the interval (-∞, ∞).

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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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