# What are the first and second derivatives of #f(x)=ln(e^-x + xe^-x) #?

##### 1 Answer

#### Explanation:

In this case, you could build the derivative immediately using the chain rule.

However, it is much easier if you simplify the function beforehand.

Let me break it down to you. :)

First, you can factor

Now, you can use the logarithm rule

As next, please remember that

This means that our function can be simplified in:

Now we can compute the derivatives. :)

Hope that this helped!