Derivative confusion

xx\in \Re f(x)=x+x+x+......x(xtimes) \\ f\left( x \right) =x+x+x+......x\quad \quad (x\quad times)\\ Thenfirstderivativeoff(x)willbexor2x?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
4 years, 4 months ago

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

Abhijeet Verma - 4 years, 4 months ago

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Is xx an integer? If not then the expression x2=x+x+x times  x^2 = x+ x+ \dots \dots x \text{ times } doesn't make sense.

Sudeep Salgia - 4 years, 4 months ago

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

Abhijeet Verma - 4 years, 4 months ago

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

Krishna Sharma - 4 years, 4 months ago

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@Krishna Sharma But x doesn't only belong to integers. xx\quad \in \quad \Re

Abhijeet Verma - 4 years, 4 months ago

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@Abhijeet Verma Try writing down the function for x=2.5 x = 2.5 .

Siddhartha Srivastava - 4 years, 4 months ago

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@Abhijeet Verma Then how can you write x2x^2 'x' times x when x is not integer?

Krishna Sharma - 4 years, 4 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 - 4 years, 4 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 - 4 years, 4 months ago

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