How Do You Derive and Simplify (1+e^-x)^-1?

[TheHamburgler1]

Homework Statement

Find the derivative of (1+e^-x)^-1

Homework Equations

The Attempt at a Solution

I can't seem to get anywhere with this. Should I be looking for a property of something like the cosh function to apply to this?

Thanks

 

[Mark44]

Homework Statement

Find the derivative of (1+e^-x)^-1

Homework Equations

The Attempt at a Solution

I can't seem to get anywhere with this. Should I be looking for a property of something like the cosh function to apply to this?

Thanks

No. Start with the chain rule.

 

[TheHamburgler1]

Of course, silly me.

So I get (e^(-x))((1+e^-x)^-2)

Can this be simplified?

-Cheers

 

[Ksitov]

Of course, silly me.

So I get (e^(-x))((1+e^-x)^-2)

Can this be simplified?

-Cheers

Hi,

I'm okay with your result.

I don't think that you can simplify.

If you look for the variation's function, it's not necessary !

(e^(-x))/(1+e^-x)^2

Because:

e^(-x) > 0 and (1+e^-x)^2 > 0