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debjit625

Member

Registered: 2012-07-23

Posts: 101

Successive differentiation

Find the value of

  for

,when 

.

In the my book  its already solved the problem is that I don't understand after a certain point ,the steps.
After solving we have

Putting x = 0

Replacing n by n-2,we get similarly

After this point /step I don't understand anymore ,here is the rest which I want you people to explain me how and why its done (which is actually my question) ...

Also   

(the first and second derivative at 0 )

Thus   

,if n is even

and 

,if n is odd

Thanks

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Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Successive differentiation

Also   

(the first and second derivative at 0 )

Thus   

,if n is even

and 

,if n is odd

I have not gone through entirely but by your own logic it should look like

,if n is even

and 

,if n is odd

Last edited by thickhead (2016-06-15 01:42:56)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

debjit625

Member

Registered: 2012-07-23

Posts: 101

Re: Successive differentiation

I also found that,I differentiate  the function upto third order and that's what the logic look likes.
But again I didnt understood the last three steps so I didn't change it . It is what written in my book.

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Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Successive differentiation

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

debjit625

Member

Registered: 2012-07-23

Posts: 101

Re: Successive differentiation

Thank you so much for the help thickhead,it solved my problem ,but one thing u said, I cant figure it out is that if

is expressed in terms of

, I guess in this problem its not possible for x = 0.

Thanks

Last edited by debjit625 (2016-06-17 10:47:12)

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Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Successive differentiation

I was talking about other recursions like n!=n*(n-1)!  and (n-1)!=(n-1)*(n-2)!  etc. Not related to your problem.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

debjit625

Member

Registered: 2012-07-23

Posts: 101

Re: Successive differentiation

Thanks

---

Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor