How do I derive y = ln(xe^x^3)? Do I do it like this:

Use the formula:

1/(xe^x^3)

Multiply it times the derivative, found using the product rule:

1/(xe^x^3) * (xe^x^3) + e^x^3

Simplify:

((xe^x^3) + e^x^3) / (xe^x^3)

Divide out e^x^3:

(x + 1)/ x

Sorry; I don't know how to make the calculations look good when typing. So, is that right? I have the feeling I did something wrong, so that's why I'm asking. Thanks!