Differentiating exponential functions

• Oct 1st 2010, 04:33 PM
blackdragon190
Differentiating exponential functions
I'm having trouble differentiating the function

$f(x)=axe^{(-bx)}$

where a and b are constants.

I'm supposed to show that the turning point occurs at

$x=1/b$

Using the product rule I get

$a(e^{-bx})+(ax)(-be^{-bx})$

But no matter what I do with that, I can't seem to get

$x=1/b$
• Oct 1st 2010, 04:40 PM
skeeter
Quote:

Originally Posted by blackdragon190
I'm having trouble differentiating the function

$f(x)=axe^{(-bx)}$

where a and b are constants.

I'm supposed to show that the turning point occurs at

$x=1/b$

Using the product rule I get

$a(e^{-bx})+(ax)(-be^{-bx})$

But no matter what I do with that, I can't seem to get

$x=1/b$

$a \cdot e^{-bx}-abx \cdot e^{-bx} = 0$

$a \cdot e^{-bx}(1 - bx) = 0$

$x = \frac{1}{b}$
• Oct 1st 2010, 04:46 PM
blackdragon190
Thank you :)