# How do you differentiate f(x)= e^x/(e^(3-x) -x ) using the quotient rule?

May 7, 2018

Just apply the quotient rule.

#### Explanation:

If you think about it, you basically have:

$f \left(x\right) = \frac{h \left(x\right)}{g} \left(x\right)$

as such, we can apply our quotient rule:

$f ' \left(x\right) = \frac{h ' \left(x\right) g \left(x\right) - h \left(x\right) g ' \left(x\right)}{g \left(x\right)} ^ 2$

and then get this:

$f ' \left(x\right) = \frac{\left({e}^{x}\right) \left({e}^{3 - x} - x\right) - \left({e}^{x}\right) \left(- {e}^{3 - x} - 1\right)}{{e}^{3 - x} - x} ^ 2$

And I'll leave the simplifying to you :)