# Thread: Differentiate ln(1+e^x) from first principles.

1. ## Differentiate ln(1+e^x) from first principles.

Hi,

First post here

Anyway, I'm currently stuck on this question and I have no idea how to get any furfther, so I would really appreciate any help with it.

Differentiate using first principles:

f(x) = ln(1+e^x)

I've managed to get to this point:

f'(x) = lim(h -> 0) (ln((e^x+e^-h)/(e(^x)+1)))/h

But I don't know how to get rid of the log, or the h's for that matter.

Cheers, Paul.

Edit: Sorry the thread title should say exponential functions, too tired.

2. Originally Posted by Intrepid44
Hi,

First post here

Anyway, I'm currently stuck on this question and I have no idea how to get any furfther, so I would really appreciate any help with it.

Differentiate using first principles:

f(x) = ln(1+e^x)

I've managed to get to this point:

f'(x) = lim(h -> 0) (ln((e^x+e^-h)/(e(^x)+1)))/h

But I don't know how to get rid of the log, or the h's for that matter.

Cheers, Paul.

Edit: Sorry the thread title should say exponential functions, too tired.
Dear Intrepid44,

Please refer the attached pdf file. If you have any questions please do not hesitate to ask me.

3. Ah, Sudharaka used the Taylor's series expansion for $\displaystyle e^x$. That's clever!

4. Originally Posted by HallsofIvy
Ah, Sudharaka used the Taylor's series expansion for $\displaystyle e^x$. That's clever!
Thanks HallsofIvy. Subscribed to this thread a couple of days ago, and thought about this problem for some time, since this is something that I havent encountered before.