Suppose I have a scalar-valued multivariate function which can be expressed as a product of simpler functions, and I want to compute something like the finite difference "gradient."
I am looking for a good reference on the mechanics of finite differences in this context, and some basic theorems about how to navigate this.
Is the partial difference gradient as well-behaved as the ordinary gradient?
What is the product rule for a large product where finite differences are concerned?
These are fairly basic questions, but I'm having trouble finding these things online. Is there a good textbook (or web page) for this material?