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

$\displaystyle x=1/b$