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Differentiating with respect to size of index

0

$begingroup$

I have the following function:
$$asum_i=1^nx_i. $$
I wish to differentiate with respect to $n$. If all $x_i$s were the same, this problem would be trivial, obviously. Can anyone help?

derivatives implicit-differentiation

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asked Mar 27 at 17:19

MathterMathter

11

$endgroup$

add a comment | 

0

$begingroup$

I have the following function:
$$asum_i=1^nx_i. $$
I wish to differentiate with respect to $n$. If all $x_i$s were the same, this problem would be trivial, obviously. Can anyone help?

derivatives implicit-differentiation

share|cite|improve this question

asked Mar 27 at 17:19

MathterMathter

11

$endgroup$

add a comment | 

$begingroup$

I have the following function:
$$asum_i=1^nx_i. $$
I wish to differentiate with respect to $n$. If all $x_i$s were the same, this problem would be trivial, obviously. Can anyone help?

derivatives implicit-differentiation

share|cite|improve this question

asked Mar 27 at 17:19

MathterMathter

11

$endgroup$

share|cite|improve this question

asked Mar 27 at 17:19

MathterMathter

11

share|cite|improve this question

asked Mar 27 at 17:19

MathterMathter

11

asked Mar 27 at 17:19

MathterMathter

11

asked Mar 27 at 17:19

MathterMathter

11

2 Answers
2

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2

$begingroup$

Depending on how deep you go into integration theory, your question may not make a lot of sense.

Notice that you are differentiating with respect to a non continous variable ($n notin mathbb R $) but to a discrete variable ($n in mathbb N $).

To go further, making sense to this differential would involve distribution theory wikipedia : Distribution

share|cite|improve this answer

answered Mar 27 at 17:49

FlorianFlorian

22614

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I suppose you could turn it into a continuous variable:
  $endgroup$
  – Mathter
  Mar 27 at 18:11
  

  
  
  
  

add a comment | 

0

$begingroup$

I suppose you could turn it into a continuous variable as follows:
$$int_0^overlinezz dz $$. differentiating this expression wrt $overlinez$ yields $overlinez$?

share|cite|improve this answer

answered Mar 27 at 18:13

MathterMathter

11

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add a comment | 

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2

$begingroup$

Depending on how deep you go into integration theory, your question may not make a lot of sense.

Notice that you are differentiating with respect to a non continous variable ($n notin mathbb R $) but to a discrete variable ($n in mathbb N $).

To go further, making sense to this differential would involve distribution theory wikipedia : Distribution

share|cite|improve this answer

answered Mar 27 at 17:49

FlorianFlorian

22614

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I suppose you could turn it into a continuous variable:
  $endgroup$
  – Mathter
  Mar 27 at 18:11
  

  
  
  
  

add a comment | 

2

$begingroup$

Depending on how deep you go into integration theory, your question may not make a lot of sense.

Notice that you are differentiating with respect to a non continous variable ($n notin mathbb R $) but to a discrete variable ($n in mathbb N $).

To go further, making sense to this differential would involve distribution theory wikipedia : Distribution

share|cite|improve this answer

answered Mar 27 at 17:49

FlorianFlorian

22614

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I suppose you could turn it into a continuous variable:
  $endgroup$
  – Mathter
  Mar 27 at 18:11
  

  
  
  
  

add a comment | 

$begingroup$

Depending on how deep you go into integration theory, your question may not make a lot of sense.

Notice that you are differentiating with respect to a non continous variable ($n notin mathbb R $) but to a discrete variable ($n in mathbb N $).

To go further, making sense to this differential would involve distribution theory wikipedia : Distribution

share|cite|improve this answer

answered Mar 27 at 17:49

FlorianFlorian

22614

$endgroup$

share|cite|improve this answer

answered Mar 27 at 17:49

FlorianFlorian

22614

answered Mar 27 at 17:49

FlorianFlorian

22614

answered Mar 27 at 17:49

FlorianFlorian

22614

0

$begingroup$

I suppose you could turn it into a continuous variable as follows:
$$int_0^overlinezz dz $$. differentiating this expression wrt $overlinez$ yields $overlinez$?

share|cite|improve this answer

answered Mar 27 at 18:13

MathterMathter

11

$endgroup$

add a comment | 

0

$begingroup$

I suppose you could turn it into a continuous variable as follows:
$$int_0^overlinezz dz $$. differentiating this expression wrt $overlinez$ yields $overlinez$?

share|cite|improve this answer

answered Mar 27 at 18:13

MathterMathter

11

$endgroup$

add a comment | 

$begingroup$

I suppose you could turn it into a continuous variable as follows:
$$int_0^overlinezz dz $$. differentiating this expression wrt $overlinez$ yields $overlinez$?

share|cite|improve this answer

answered Mar 27 at 18:13

MathterMathter

11

$endgroup$

share|cite|improve this answer

answered Mar 27 at 18:13

MathterMathter

11

answered Mar 27 at 18:13

MathterMathter

11

answered Mar 27 at 18:13

MathterMathter

11