# Homework Help: F(x)=2xe^(-x) what is derivative?

1. Dec 15, 2004

### UrbanXrisis

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

what is derivative?

$$f(x)=(2x)/(e^x)$$
$$f'(x)={{2e^x}-{2x^2e^{x-1}}}/(e^x)^2$$

can I simplify this?

2. Dec 15, 2004

### Integral

Staff Emeritus
Recall that:
$$\frac {d e^x} {dx} = e^x$$
then apply the chain rule.

Last edited: Dec 15, 2004
3. Dec 15, 2004

### FZ+

Surely easier to do by product rule!

$$f'(x)=2e^-^x - 2xe^-^x$$

or even:

$$f'(x)=(2 - 2x)e^-^x$$

Last edited: Dec 15, 2004
4. Dec 15, 2004

### UrbanXrisis

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?