There are a lot of subscripts and functions that make this look harder than it really is.

You have:

Now you want to take the partial derivative with respect to . In other words, you want to see how changes when changes and all the other variables are held constant.

Assuming you can exchange the derivative with the integral,

Since doesn't vary with respect to , we can treat it like a constant. The derivative of a constant times a function is the constant times the derivative:

And lastly, is a constant, so the derivative of a function minus a constant is just the derivative of that function:

And I assume that in your notation, and , so the result is:

- Hollywood