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Where is the mistake?

\[\underbrace{x+x+x+x+\cdots+x}_{x \times x } = x^{2}\]

Differentiating both sides with respect to \(x\)

\[\underbrace{1+1+1+1+\cdots+1}_{x \times 1 } = 2x\]

\[\implies x=2x\]

Note by Hritesh Mourya
2 months, 2 weeks ago

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Equation 1 is only true when \(x\) is an positive integer. It is not continuous and therefore non-differentiable. Therefore, equation 2 does not apply. Chew-Seong Cheong · 2 months, 2 weeks ago

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@Chew-Seong Cheong Thanks a lot Hritesh Mourya · 2 months, 2 weeks ago

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@Chew-Seong Cheong Absolutely perfect.@Hritesh Mourya here is your answer Satyabrata Dash · 2 months, 2 weeks ago

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How many times does this question keep popping up? @Calvin Lin

In one month I've seen two of these. Can't it added to the misconceptions page? Deeparaj Bhat · 2 months, 2 weeks ago

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