# Differentiating exponential functions

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

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

where a and b are constants.

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

$\displaystyle x=1/b$

Using the product rule I get

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

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

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

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

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

where a and b are constants.

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

$\displaystyle x=1/b$

Using the product rule I get

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

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

$\displaystyle x=1/b$

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

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

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