F(x)=2xe^(-x) what is derivative?

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Homework Help Overview

The discussion revolves around finding the derivative of the function f(x) = 2xe^(-x) and exploring its critical points to determine relative extrema.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss different methods for finding the derivative, including the product rule and chain rule. There is also an inquiry about simplifying the derivative expression.

Discussion Status

Some participants have provided alternative derivative expressions and methods, while one participant has attempted to analyze critical points and determine the nature of the extrema. There is an ongoing exploration of the implications of the derivative.

Contextual Notes

One participant notes that the original question involves finding critical points and assessing whether they represent relative maxima or minima, indicating a broader scope beyond just differentiation.

UrbanXrisis
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f(x)=2xe^(-x)

what is derivative?

[tex]f(x)=(2x)/(e^x)[/tex]
[tex]f'(x)={{2e^x}-{2x^2e^{x-1}}}/(e^x)^2[/tex]

can I simplify this?
 
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Recall that:
[tex]\frac {d e^x} {dx} = e^x[/tex]
then apply the chain rule.
 
Last edited:
Surely easier to do by product rule!

[tex]f'(x)=2e^-^x - 2xe^-^x[/tex]

or even:

[tex]f'(x)=(2 - 2x)e^-^x[/tex]
 
Last edited:
gee thanks!
The questions acually asks to find each critical point of f and whether f(x) is a relative maximum, relative minimum, or neither. I set f'(x) to zero and solved. I got x=1.

I found it to be a maximum value. Is this correct?
 

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