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The error must be associated with the limitations on the application of derivatives! (mander.xyz)

submitted 4 days ago by [email protected] to c/[email protected]

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[–] [email protected] 8 points 3 days ago* (last edited 3 days ago)

Because differentiation needs the expression to be continuous. And x + x + x … x times is not continuous.

Derivates are built on limits, which assume the function is continuous. ie. it gives an output for every single Real number, even decimals.

This is the case for x^2 but not x + x + x … x times. Here you’re only adding one x every full number. So the function is discrete, a value only exists every full number. You cannot express something you wish to differentiate this way.

ELI5: x^2 and x + x + x … x times are only equal if you use full positive numbers, ie. 1, 17,

if you use decimal numbers or negative numbers x + x + x … x times is undefined.

This means it cannot be differentiated.