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

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Homework Help Overview

The problem involves finding the derivative of the function (1+e^-x)^-1, which falls under the subject area of calculus, specifically differentiation of functions involving exponential terms.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants express difficulty in deriving the function and consider whether properties of hyperbolic functions, such as cosh, might be relevant. There is also a mention of applying the chain rule as a potential starting point.

Discussion Status

Some participants have shared their results and are questioning the possibility of further simplification. Guidance has been offered regarding the validity of the derived expression, with one participant indicating that simplification may not be necessary.

Contextual Notes

There appears to be some uncertainty regarding the need for simplification and the relevance of certain mathematical properties. The discussion reflects a lack of consensus on the necessity of further steps in the problem-solving process.

TheHamburgler1
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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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