confusing problem has me stuck

I have a sample of observations,(j1,j2,j3........jn) each can have the value 0 or 1

The probability of the yth member of the sample being 1 is given as

Where x is an unknown constant, and is a variable, but known for each member of the sample.

How can I find x?

The probability of the sample turning out the way it did is

This formula F will change depending on what x is, so I think i need to calculate the likelyhood of x = some value, and then calculate the max likelyhood of x, but I am stuck at how to get there. On wikipedia, there is an example half way down the page of calculating the max likelyhood for a continuous distribution, continuous parameter space, but I cant see how to use this in my example

Thanks for any help, hope this makes sense and the formulas are readable