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