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A paradox with derivatives


Best Answer vigmeister, 05 May 2013 - 08:03 AM

Spoiler for mathematical representaiton

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#1 BMAD

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Posted 05 May 2013 - 01:02 AM

The derivative of x2, with respect to x, is 2x.  However, suppose we write x2 as the sum of x x's, and then take the derivative:

Let f(x) = x + x + ... + x  (x times)

 

Then f'(x)

= d/dx[x + x + ... + x]  (x times)

 

= d/dx[x] + d/dx[x] + ... + d/dx[x]  (x times)


     

= 1 + 1 + ... + 1  (x times)

 

  = x

This argument appears to show that the derivative of x2, with respect to x, is actually x.  Where is the fallacy?


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#2 vigmeister

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Posted 05 May 2013 - 08:03 AM   Best Answer

Spoiler for mathematical representaiton


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#3 dark_magician_92

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Posted 05 May 2013 - 11:37 AM

Spoiler for


Edited by dark_magician_92, 05 May 2013 - 11:38 AM.

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#4 bonanova

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Posted 05 May 2013 - 11:07 PM

vigmester - nice solve.

This is one of the better puzzles of the "find the fallacy" genre.

 

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