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

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Started by BMAD, May 05 2013 01:02 AM

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

Spoiler for mathematical representaiton

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3 replies to this topic

Posted 05 May 2013 - 01:02 AM

The derivative of x^{2}, with respect to x, is 2x. However, suppose we write x^{2} 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 x^{2}, with respect to x, is actually x. Where is the fallacy?

Posted 05 May 2013 - 08:03 AM Best Answer

Spoiler for mathematical representaiton

Posted 05 May 2013 - 11:37 AM

Spoiler for

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

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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