So to be clear, the question is:How do I calculate the Jacobian matrix of?

Edit:To start off simpler, can someone please tell me how to calculate the Jacobian martix of ? The Jacobian of r is the unity matrix, , and the Jacobian of v is the zero matrix.

Edit 2:The final expression in my previous post is supposed to equal the Jacobian matrix, not the transpose of the Jacobian matrix.