Suppose we have functional $m(z,\gamma(x_{1},x_{2}))=\frac{C(z)\int\gamma(x_1,x_2)dx_1}{\gamma(x_1,x_2)}$, where $C(z)$ could be considered a constant (it doesn't change with $x_1,x_2$), $\gamma(x_1,x_2)$ is a smooth nonzero function and $(x_1,x_2)\in\mathcal{X}\subset R^2$.
What is the Frechet derivative of $m(z,\gamma(x_{1},x_{2}))$ with respect to $\gamma(x_{1},x_{2})$? It would be great if you could explain why we are doing each step in your derivation, as the idea of Frechet derivative is completely new to me. Thanks!