Find the derivative of each function.

Answer

- This function has two products inside a quotient. Overall, we want to use the quotient rule:

However, in order to do this we need to find the derivatives of the numerator and the denominator, each of which requires the product rule.

Now for the quotient rule:

We want to simplify as much as is reasonable, but not too much. In this case the denominator isn't too bad to multiply out, so we'll do that:

We notice that e^{x} is common to every term in the numerator, and is also in the denominator:

We can cancel out e^{x}. We will still have one occurrence of e^{x} in the denominator, since the denominator previously contained

(e^{x})^{2}:

We'll stop here, because if we multiply stuff out we'll be doing more unnecessary steps.