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**Gautam****Guest**

I have a problem related to derivatives....Please email me the solution, if possible

Problem:

**X+X+X……..Xtimes = X^2** …..{e.g. 5+5+5+5+5 (5 times 5)equals to 5^2}

Taking derivative d/dX on both sides

**d/dX (X+X+X……..Xtimes) = d/dX (X^2)**

**1+1+1…..Xtimes = 2X** ……..(derivative of x^2 = 2x and of x is 1)

Ergo, **X=2X** ?????.......How come???

**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 121

The fallacy is that you are differentiating wrt x, but your function is not definded until x itself is defined, but then x will be a constant. Moreover: in d/dX (X+X+X ..Xtimes) the "function" in the brackets is NOT defined at the time of differentiation and so cannot be differentiated.

For a different way of saying this see http://www.qbyte.org/puzzles/p032s.html

Mitch

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,654

That is correct. "(X+X+X ..Xtimes)" is a function! If you are going to evaluate it first, then you have to evaluate the other side too.

Valid:

(X+X+X
..Xtimes) = X^2

Valid:

(4+4+4+4) = 4^2

Invalid:

(4+4+4+4) = X^2

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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