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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, 3 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. Abhijeet Verma · 2 years, 3 months ago

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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. Sudeep Salgia · 2 years, 3 months ago

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@Sudeep Salgia If we don't restrict x to integers ,then ? (Addition of continuous functions should yield a continuous function ) Abhijeet Verma · 2 years, 3 months ago

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@Abhijeet Verma If x is an integer then function won't be continuous hence Differentiating it would be meaningless. Krishna Sharma · 2 years, 3 months ago

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@Krishna Sharma But x doesn't only belong to integers. \[x\quad \in \quad \Re \] Abhijeet Verma · 2 years, 3 months ago

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@Abhijeet Verma Then how can you write \(x^2\) 'x' times x when x is not integer? Krishna Sharma · 2 years, 3 months ago

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@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 Abhijeet Verma · 2 years, 3 months ago

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@Abhijeet Verma Try writing down the function for \( x = 2.5 \). Siddhartha Srivastava · 2 years, 3 months ago

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@Sandeep Bhardwaj sir , @Brian Charlesworth sir and @Azhaghu Roopesh M please help. Abhijeet Verma · 2 years, 3 months ago

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