Derivative of dW and db

I think I have fully understood week-3 except one really simple thing.

image

The video does not explain how they came up with these derivatives. (I have zero formal background in calculus, learning myself).

The way I think about this is

Z = Wx + b
partial derivative of w / Z is dz = dWx (b is dropped since it is a constant)
so dW = dZ / x ie. dZ * x.T

partial derivative of b / Z is dz = db (dWx is dropped since it is a constant)
which matches with the screenshot db = dZ.

Am I correct? if not, can someone please explain? Or point out the segment in the video where this derivative is discussed.

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Please check this YouTube guide of Eddy Shyu.

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Thanks, I still dont get the db explanation but I will watch a couple of times till it sinks in