Help Solving a Boundary Integral Equation for the Acoustic Analysis of a Quadratic Residue Diffuser-Topped Sound Barrier

it has been a while since I’ve attempted partial derivatives but I am hoping that someone can help guide me in the right direction so that I can solve a specific equation that attempts to calculate the sound pressure at a receiver from a source with a quadratic residue diffuser between them.

Below is an example of the configuration I am trying to analyze:

A Quadratic Residue Diffuser similar to the image below would be placed on top of the Sound Barrier:

Now, from research papers I have concluded that in order to find the Sound Pressure at the receiver location (a point behind the sound barrier), I must solve the following Boundary Integral Equation:

Where:

Since my sound source will be on the ground surface ro’ will be equal to ro.

I will be analyzing a receiver positioned in the propagating medium.

The integral gamma is equal to n (the number of wells on the QRD surface)

I believe I have already figured out how to compute most of the equation. Where I need help is in understanding how to compute the partial derivative portion of the equation.

I am using Wolfram Mathematica for computation, but I’m not sure how to input the partial part of the equation.

Any help would be appreciated and I will answer any questions I can.

Thank you.