I never said I didn’t remember how to differentiate multivariate functions - my point was that equating conceptual mathematical knowledge and the ability to implement a specific application of such concepts in a time-constrained and stressful situation is inappropriate.

A lot of things need to come together in answering a question like this - remembering that the chain rule is the key concept in backprop the first place, knowledge of how to implement matrix algebra in code, knowing the commonly-used loss functions, how to compute their derivatives, and how to represent the differentiation in code, etc. None of these things is complicated on its own; the difficulty arises in bringing everything together in a small amount of time. It’s fair to expect people in the field to intuitively remember what is going on but on the spot implementation in under 30 minutes requires a level of rigor that is unrealistic for even a competent person who does not have the theory fresh in their memory.

You keep using the term ‘smart’ and I don’t know what you mean by this. Your last statement is just an assertion without argument, one you’ve repeated throughout your comments but I see no reason to believe, given the above.