Here’s a thread with some links, but I think they only cover the derivations for FC nets and ConvNets. The thread links to a bibliography thread which points to books like Goodfellow et al which might cover this, but I have not actually looked at it to check that.
Note that Stanford has been very generous about putting material from their ML related courses online. The previous linked thread points to CS231, which covers ConvNets. You might check CS224n, which is their intro NLP course. That would involve RNNs, so might include those derivations.