Differentiating exponential functions

**blackdragon190** · October 1st 2010, 04:33 PM

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

$x=1/b$

**skeeter** · October 1st 2010, 04:40 PM

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

$x=1/b$