# 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 years 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.

- 2 years ago

Thanks a lot

- 2 years ago

Comment deleted 1 month ago

- 1 year, 9 months ago

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?

- 2 years ago