Derivation of dZ^[1]

Course Q&A Deep Learning Specialization Neural Networks and Deep Learning
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The following question is in reference to Course 1, week 4:

I’ve gone through the lectures several times now, and I haven’t seen the derivation of dZ^[1]. It’s also not covered in the “Backpropagation Intuition (Optional)” video. The equation is presented, but its derivation is never discussed. It’s an element-wise multiplication of two matrices and its form completely breaks the symmetry of the other gradient equations.

The equation in question is as follows:
dZ^[1] = ((W^[2]).T) (dZ^[2]) * g’(Z^[1]), where * is element-wise multiplication

What is ((W^[2]).T) (dZ^[2])? I’ve not seen W.T multiply dZ at any other point in the course.

Was this derivation intentionally skipped because of its difficulty level? Can you point me to a reference in which this gradient is derived? I’d really like to complete the picture on its derivation. Thanks in advance.

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Hi @wmartin,

try to take a look at this link Course 1: Week 3 (backpropagation intuition) where we have already talked about this topic.
I hope it answers your question.

Best,
Alessandra

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@alessandra Thank you! The post by Yaswanth64 cleared everything up for me.

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