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)`

?

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)`

?

1 Like

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)`

?

1 Like

No worries. I’ve requested the staff to take your suggestion into account and improve the lecture. Thanks for bringing this up.

1 Like