How to calculate this partial derivative? given the function: v h </msub> =

uplakanimkk 2022-07-15 Answered
How to calculate this partial derivative?
given the function:
v h = [ i = 1 N r h , i w h , i 1 T t = 1 T i = 1 N r t , i w t , i ] 2
I would like to compute the following:
v h w h = ?
v h r h = ?
v h w h r h = ?
The problem for me is the double sum in the second term. Example of the function with N = 2 and T = 2 for t = 1:
v 1 = [ ( r 1 , 1 w 1 , 1 + r 1 , 2 w 1 , 2 ) 1 2 ( r 1 , 1 w 1 , 1 + r 1 , 2 w 1 , 2 + r 2 , 1 w 2 , 1 + r 2 , 2 w 2 , 2 ) ] 2
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Answers (1)

Zane Barry
Answered 2022-07-16 Author has 5 answers
Step 1
Let denote your function as v t = y t 2 where
y t = r t : w t 1 T r t : w t + C
Step 2
The colon operator denotes the inner product between vectors and C is a constant that does not depend on r t , w t . It follows using chain rule that v t w t = 2 y t ( 1 1 T ) r t .

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