Homework Help: Is this derivative correct?

1. Mar 14, 2007

linuxux

1. The problem statement, all variables and given/known data

Find derivative of function: $$f\left(x\right)=\frac{1}{1+e^{x}}$$

2. Relevant equations

quotient rule.

3. The attempt at a solution

hopefully this is the solution:
$$f^{'}\left(x\right)=\frac{e^{x}}{(1+e^{x})^{2}}$$

Last edited: Mar 14, 2007
2. Mar 14, 2007

d_leet

Really close, but not exactly. Are you sure about the denominator? How is it different from that of the original function?

3. Mar 14, 2007

linuxux

oh, thanks! i had that messed up on my paper too.

4. Mar 14, 2007

dextercioby

The derivative is okay up to the overall "-" sign which should be absent in the numerator.

5. Mar 14, 2007

linuxux

i think its fixed now...

6. Mar 14, 2007

dextercioby

Still incorrect. Remember that

$$\frac{d}{dx}\left(\frac{1}{f(x)}\right)=-\frac{f'(x)}{f^{2}(x)}$$

7. Mar 14, 2007

linuxux

oh, i know this should be easy but i've been studying calculus for only 48 hours, so i appreciate the patience and help.

I could easily rewrite the equation like this $$(1+e^{x})^{-1}$$ and derivate it, but i should know how to do it the other way.

Last edited: Mar 14, 2007