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# Derivative confusion

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

Note by Abhijeet Verma
2 years, 6 months ago

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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.

- 2 years, 6 months ago

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

- 2 years, 6 months ago

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

- 2 years, 6 months ago

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

- 2 years, 6 months ago

But x doesn't only belong to integers. $x\quad \in \quad \Re$

- 2 years, 6 months ago

Then how can you write $$x^2$$ 'x' times x when x is not integer?

- 2 years, 6 months ago

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

- 2 years, 6 months ago

Try writing down the function for $$x = 2.5$$.

- 2 years, 6 months ago