You could do this but I'm pretty sure that real AD just deals all the common primitives directly. The derivative of sin(x) is cos(x), etc. AD just postpones the

You could do this but I'm pretty sure that real AD just deals all the common primitives directly. The derivative of sin(x) is cos(x), etc. AD just postpones the chain rule calculations that would be involved in something sin(x + x^2)^2, so the chain-rule happens at run time instead of a symbol expansion at compile time.