$x\in \Re$$\\ f\left( x \right) =x+x+x+......x\quad \quad (x\quad times)\\$$Then\quad first\quad derivative\quad of\quad f\left( x \right) \quad will\quad be\quad x\quad or\quad 2x?$
The confusion arrived due to a problem similar to it.

@Krishna Sharma
–
Yeah , adding x times x itself implies that x has to be a whole number. Thus its differentiation would have no meaning.Thanks and sry

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## Comments

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TopNewest@Sandeep Bhardwaj sir , @Brian Charlesworth sir and @Azhaghu Roopesh M please help.

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Is $x$ an integer? If not then the expression $x^2 = x+ x+ \dots \dots x \text{ times }$ doesn't make sense.

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If we don't restrict x to integers ,then ? (Addition of continuous functions should yield a continuous function )

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If x is an integer then function won't be continuous hence Differentiating it would be meaningless.

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$x\quad \in \quad \Re$

But x doesn't only belong to integers.Log in to reply

$x = 2.5$.

Try writing down the function forLog in to reply

$x^2$ 'x' times x when x is not integer?

Then how can you writeLog in to reply

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y=x is a continuous function. Thus, y=x+x+x+....x will also be a continuous function for all x belongs to real.

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