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A paradox with derivatives
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)
= d/dx[x + x + ... + x] (x times)
= d/dx[x] + d/dx[x] + ... + d/dx[x] (x times)
= 1 + 1 + ... + 1 (x times)
This argument appears to show that the derivative of x2, with respect to x, is actually x. Where is the fallacy?
Posted 05 May 2013 - 11:37 AM
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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