Consider the equattion X+X+X...(X TIMES).. 2+2=2^2 3+3+3=3^2
similarly x+x+x+x...(x times)=x^2
Now Differentiate on both side with respect to x 1+1+1...x times = 2x =x=2x =>1 =2
What is the mistake here??any idea? [ March 13, 2006: Message edited by: Rambo Prasad ]
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Ulf Dittmer
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The equality is not true (or rather, is not defined) for numbers that are not integers. And since differentiation is defined only for continuous functions -which the one on the LHS is not- it can't be applied here.
Another explanation: x^2 might be a notation for a function x^2. But you use it as a value (x^2=x | x=1). Then you mix both notations, but you may not differentiate a value.
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