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September 23rd, 2012, 07:36 AM   #1
 
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Find the n'th derivative of a function

The question asks:
Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

the function is
So I need to find the function

So if I start taking the derivative I get:




so on and so forth. I see the pattern, but I really don't know the notation to write it out as one function.
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September 23rd, 2012, 07:42 AM   #2
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Re: Find the n'th derivative of a function

Quote:
Originally Posted by jaredbeach
The question asks:
Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

the function is
So I need to find the function

So if I start taking the derivative I get:




so on and so forth. I see the pattern, but I really don't know the notation to write it out as one function.
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September 23rd, 2012, 07:53 AM   #3
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Re: Find the n'th derivative of a function

Yes, the factorial is one way to go. Another is the permutation function:

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September 23rd, 2012, 01:07 PM   #4
 
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Re: Find the n'th derivative of a function

Quote:
Originally Posted by zaidalyafey
Quote:
Originally Posted by jaredbeach
The question asks:
Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

the function is
So I need to find the function

So if I start taking the derivative I get:




so on and so forth. I see the pattern, but I really don't know the notation to write it out as one function.
So is the answer?
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September 23rd, 2012, 01:24 PM   #5
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Re: Find the n'th derivative of a function

Where means to take the next derivative. This notation is NOT standard and is used for illustration only:



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September 23rd, 2012, 01:47 PM   #6
 
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Re: Find the n'th derivative of a function

Oh! so it's just ?
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September 23rd, 2012, 02:00 PM   #7
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Re: Find the n'th derivative of a function

Quote:
Originally Posted by jaredbeach
Quote:
Originally Posted by zaidalyafey
Quote:
Originally Posted by jaredbeach
The question asks:
Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.

the function is
So I need to find the function

So if I start taking the derivative I get:




so on and so forth. I see the pattern, but I really don't know the notation to write it out as one function.
So is the answer?
I suspect what you meant is:

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