# What is the derivative of #ln((e^x)/(1+e^x))#?

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You can bypass using the quoitient rule for derivatives by using the quotient rule for logarithms

In your case, you will have

You have

and

The target derivative will thus be

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The derivative of ln((e^x)/(1+e^x)) is:

1/(1+e^x)

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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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