Derivatives of SetsSo, I often see this: D x [ ∫ f ( x ) ] = f ( x )But this is a derivative of a set of antiderivatives. What is the conceptual backing for this i.e. what does it mean to derive a set?

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Derivatives of SetsSo, I often see this:      D    x        [    ∫    f    (    x    )    ]    =  f  (  x  )But this is a derivative of a set of antiderivatives. What is the conceptual backing for this i.e. what does it mean to derive a set?

Glenn Ware · Accepted Answer

Step 1Truthfully, you don&#039;t use indefinite integrals that much. You almost always will deal with an integral with limits of integration.Step 2To expand on Robert&#039;s answer, the &quot;derivative, f(x) of a set, S&quot; is the unique function such that for all   F  (  X  )  ∈  S,       F    ′    (  x  )  =  f  (  x  ).

Derivatives of Sets So, I often see this: D x </msub> [ ∫<!

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