# Why is the derivative of #ln -x = 1/x#?

This is because the chain rule says:

So:

For the same reason in this integral:

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The derivative of ln(-x) is 1/x because ln(-x) is the natural logarithm of -x, and its derivative is the reciprocal of the argument, which is 1/x. This is a consequence of the chain rule and the derivative of the natural logarithm function.

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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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