# Math Help - First and Second Derivatives and other aspects of a function

1. ## First and Second Derivatives and other aspects of a function

f(x)= 5xe^-.2x

Domain of the function = All real numbers
Intercepts: x=0 y=0
Vertical asymptote = none
Horizontal asymptote = y=0
Find f'(x) = 5/.2e^.2x

Let me know if I'm doing anything wrong so far. Thanks, appreciate all help

2. Everything looks fine except for the derivative.

$f(x) = 5xe^{\frac{-x}{5}}$
$\implies f'(x) = 5e^{\frac{-x}{5}} + 5x\frac{-1}{5}e^{\frac{-x}{5}}$ by the product rule.

It can be simplified further.

3. Thanks, mind simplifying for me?

4. I also need 2nd derivative.

5. Originally Posted by Zabulius
Thanks, mind simplifying for me?
Why don't you try it and show me your result?

6. (5e^-x/5)(1+-1/5x)

7. Originally Posted by Zabulius
(5e^-x/5)(1+-1/5x)
Let's try again

$f'(x) = 5e^{\frac{-x}{5}} + 5x\frac{-1}{5}e^{\frac{-x}{5}} \implies e^{\frac{-x}{5}} (5-x)$