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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???
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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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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