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0

$begingroup$

I have an equation where:

$J_t = frac12sum(haty-y)^2$ where $haty$ is a vector of $hat y_1,hat y_2,...hat y_k$.

If i were to differentiate $J_t$ in terms of $y_1$, is it right to assume that the $sum$ symbol doesn't affect the differentiation process?

Hence,

$fracpartial J_tpartial y_1 = (hat y_1 - y)$

I would like to know if the above is a correct way to differentiate?

discrete-mathematics partial-derivative

share|cite|improve this question

asked Mar 30 at 3:42

MaxxxMaxxx

1255

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, if you pull the first addendum it would be this: $frac12(haty_1-y)^2+sumfrac12(haty_2-y)^2$ the second part of the sum, as you can see, is a constant in $haty_1$.
  $endgroup$
  – Bertrand Wittgenstein's Ghost
  Mar 30 at 4:11
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I have an equation where:

$J_t = frac12sum(haty-y)^2$ where $haty$ is a vector of $hat y_1,hat y_2,...hat y_k$.

If i were to differentiate $J_t$ in terms of $y_1$, is it right to assume that the $sum$ symbol doesn't affect the differentiation process?

Hence,

$fracpartial J_tpartial y_1 = (hat y_1 - y)$

I would like to know if the above is a correct way to differentiate?

discrete-mathematics partial-derivative

share|cite|improve this question

asked Mar 30 at 3:42

MaxxxMaxxx

1255

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, if you pull the first addendum it would be this: $frac12(haty_1-y)^2+sumfrac12(haty_2-y)^2$ the second part of the sum, as you can see, is a constant in $haty_1$.
  $endgroup$
  – Bertrand Wittgenstein's Ghost
  Mar 30 at 4:11
  
  

  
  
  
  

add a comment | 

$begingroup$

I have an equation where:

$J_t = frac12sum(haty-y)^2$ where $haty$ is a vector of $hat y_1,hat y_2,...hat y_k$.

If i were to differentiate $J_t$ in terms of $y_1$, is it right to assume that the $sum$ symbol doesn't affect the differentiation process?

Hence,

$fracpartial J_tpartial y_1 = (hat y_1 - y)$

I would like to know if the above is a correct way to differentiate?

discrete-mathematics partial-derivative

share|cite|improve this question

asked Mar 30 at 3:42

MaxxxMaxxx

1255

$endgroup$

share|cite|improve this question

asked Mar 30 at 3:42

MaxxxMaxxx

1255

share|cite|improve this question

asked Mar 30 at 3:42

MaxxxMaxxx

1255

asked Mar 30 at 3:42

MaxxxMaxxx

1255

asked Mar 30 at 3:42

MaxxxMaxxx

1255