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## #1 2006-02-23 00:59:14

Gautam
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### Calculus Problem

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???

## #2 2006-02-23 02:08:02

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

### Re: Calculus Problem

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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## #3 2006-02-23 08:53:05

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: Calculus Problem

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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