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This is my question. Suppose that I have a continuum of people on the measure [0,1]. Then, I want to aggregate their spending as follows,

[itex]\int^{1}_{0}(s^{\alpha}(i))di[/itex]

where i is any person in [0,1]. Suppose that I want to compute the derivative of the previous expression if [itex]s^{\alpha }[/itex] goes up for only one specific i[itex]\in[0,1][/itex]. That is, I want,

[itex]\frac{d(\int^{1}_{0}(s^{\alpha}(i))di)}{d(s(i))}[/itex]

How can I compute that derivative...? First, I thought that it would be zero since the contribution to the integral is infinitesimal, but I am not sure about that...

Thank you!

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# Derivative of an integral

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