# How do you use the Product Rule to find the derivative of f(x)=e^(4-x)/6?

Aug 3, 2015

#### Answer:

$f ' \left(x\right) = - \frac{{e}^{4 - x}}{6}$

#### Explanation:

To use the product rule we need two functions of $x$, let's take:

$f \left(x\right) = \frac{{e}^{4 - x}}{6}$

=>

$f \left(x\right) = g \left(x\right) h \left(x\right)$

With:

$g \left(x\right) = {e}^{4} / 6$ and $h \left(x\right) = {e}^{-} x$

The product rule states:

$f ' = g ' h + h ' g$

We have:
$g ' = 0$ and $h ' = - {e}^{-} x$

Therefore:

$f ' = \left(0\right) \left({e}^{-} x\right) + \left({e}^{4} / 6\right) \left(- {e}^{-} x\right) = - \frac{{e}^{4 - x}}{6}$