Derivative of a functional

Question

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., $$\frac{\partial}{\partial x}\Big[\mathcal{F}[\rho(x,t)]\Big]$$