If a functional is defined as follows $$\mathcal{F}[\rho(x,t)]=\int_0^{t}w(x,\tau)\rho(x,t)d\tau$$ what is the derivative of this functional with respect to $x$ i.e., $$\frac{\partial}{\partial x}\Big[\mathcal{F}[\rho(x,t)]\Big]$$
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1Derivating under the integral sign, $$\int_0^{t}\left(w_x(x,\tau)\rho(x,t)+w(x,\tau)\rho_x(x,t)\right)d\tau$$ – Oct 18 '16 at 13:12
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@YvesDaoust: Thanks a lot. Can you point me to some literature so I can read more about it? – Rhinocerotidae Oct 18 '16 at 13:18
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1https://en.wikipedia.org/wiki/Leibniz_integral_rule – Oct 18 '16 at 13:21