How would you write this equation in MATLAB? (challenging!)

Hello guys,

I would like to put this equation into the MATLAB to calculate the global maximum of mutual information function. In order to do that, I notice that I need a gradient of the function which is described as in attached files.

I do have the vector for P(x) and P(x|spike). Let's say they are called A and B respectively. Then, how do I write this down in MATLAB to calculate the gradient?

FYI, A and B are 1-by-100 vectors.