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

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The derivative of the function (1 + e^-x)^-1 is derived using the chain rule, resulting in the expression (e^(-x))((1 + e^-x)^-2). Further simplification is not necessary, as the components e^(-x) and (1 + e^-x)^2 are always positive. The discussion confirms that the derivative can be expressed as (e^(-x))/(1 + e^-x)^2 without any further simplification required.

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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
 
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TheHamburgler1 said:

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.
 
Of course, silly me.

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

Can this be simplified?

-Cheers
 
TheHamburgler1 said:
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
 
Last edited:

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