# How do you find the derivative of #ln(e^x+1)#?

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To find the derivative of ( \ln(e^x + 1) ), you can use the chain rule. The derivative is:

[ \frac{d}{dx} \left( \ln(e^x + 1) \right) = \frac{1}{e^x + 1} \cdot \frac{d}{dx}(e^x + 1) ]

Now, differentiate ( e^x + 1 ) with respect to ( x ):

[ \frac{d}{dx}(e^x + 1) = e^x ]

Substitute this result back into the expression:

[ \frac{d}{dx} \left( \ln(e^x + 1) \right) = \frac{1}{e^x + 1} \cdot e^x ]

Simplify:

[ \frac{d}{dx} \left( \ln(e^x + 1) \right) = \frac{e^x}{e^x + 1} ]

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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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