In reply to Erkki S.

1) As I say in paragraph 2, I'm not computing the gradient of the density, I am computing the gradient of the CUMULATIVE distribution function. The gradient of the density is easy and well known.
2) You are thinking of derivatives with respect to parameters. I am taking derivatives w.r.t x. By the chain rule d/dx( log(F(x,y) ) = 1/f(x,y) * dF/dx. Therefore using the log doesn't prevent needing to know dF/dx.
3) To answer your question, I am finding the gradient because next week I'm going to show how to compute specific contours of the cumulative distribution function.