This is not difficult but a little bit long to write.
What is your objective?
Is it for some homework, or do you have a practical application?
For an homework, the result would not be helpful for you, only the method matters.
There are only known functions in this expression: products, divisions, logarithm, exponential.
Reading a table of derivatives rules and a bit of patience is enough.
On wiki you can find the basis about derivatives and the http://en.wikipedia.org/wiki/Derivative" [Broken].
For a practical application, more details would be needed to decide how to proceed for the best result.
If this derivative is the only one in the project, then using a software like Mathematica could avoid any typing error.
If you only need numerical results, then "Numerical Recipes" explains what to care for.