Why does the formula for dJ/db skip the term dv/du?
In the lecture, dJ/db = (dJ/du)*(du/db)
Shouldn’t it be: dJ/db = (dJ/du)*(dv/du)*(du/db)?
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We can see that \frac{dv}{du} = 1
Yes, I understand. I was just expecting this term (dv/du) to be explicitly mentioned in the formula, together with the other terms. Otherwise it is a bit confusing, whether it is generally skipped, or whether we just do not bother writing it in the case of it being equal to 1.
Your first 2 terms in the bottom expression are incorrect. The lecture is correct.
Here’s how to do it:
\frac{dJ}{db} = \frac{dJ}{dv} . \frac{dv}{du} . \frac{du}{db}
\Rightarrow \frac{dJ}{db} = \frac{dJ}{du} . \frac{du}{db}
Please see this link to understand how \frac{du}{db} was computed using the limit approach.
Ah, yes! I was actually meaning to write:
Shouldn’t it be:
dJ/db = (dJ/dv)*(dv/du)*(du/db)?
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No worries. I’ve requested the staff to take your suggestion into account and improve the lecture. Thanks for bringing this up.
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