Quick question on typical integration/differentiation. What is the justification for differentiating some integrals with respect to constants in order to obtain results for them, i.e. [itex]\frac{∂}{∂α}[/itex][itex]\int e^{-αx^{2}}dx=\int-x^{2}e^{-αx^{2}}dx[/itex]? It seems to me α is a constant, so it seems a little confusing to even talk about the partial derivative. I guess if you treat the entire integral to be a multivariable function of both x and α, [itex]f(x,α)[/itex] then it's somewhat justified, though I could just as well replace alpha with some number and we'd be stuck with something like [itex]\frac{∂}{∂8}[/itex] which seems very sketchy.(adsbygoogle = window.adsbygoogle || []).push({});

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# Differentiating with respect to a constant

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