Is this derivative correct?

[linuxux]

Homework Statement

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

Homework Equations

quotient rule.

The Attempt at a Solution

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

 

[d_leet]

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

 

[linuxux]

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

 

[dextercioby]

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

 

[linuxux]

i think its fixed now...

 

[dextercioby]

Still incorrect. Remember that

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

 

[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.