Hi
I needed help understand the partial derivatives of a solution.
I have been given the chain rule.
I have attached my problem.
What concrete doubts have you had?
Fernando Revilla
Remember that each of those derivatives involves a derivative of a product and so, by the product rule, the sum of two terms. That's why, in the top line, you have four terms but in the next eight. Each of the terms you have in red for is the result of applying the derivative to the part of the product that does not already involve a derivative of u.
The first term in red I wouldn't have written at all. It is from applying the derivative in to the in : . But u and r are independent variables: so that is . That " " is times 0, not " of 0".
The second term is red is from applying the derivative in to the in : .
The third is from applying the derivative in to the in :
The fourth is from applying the derivative in to the in :
In the last, you have encircled two separate terms from two separate derivatives.
The first, , is from applying the derivative in to the in : .
The second, , is from applying the derivative in to the
in :