# How can I prove/understand the following functional derivative? [duplicate]

Assume that $$F[h(\xi);x,y]$$ be the inverse of $$G[h(\xi);x,y]$$ in the sense that the following identity is satisfied: $$$$\int dz F[h(\xi);x,z]G[h(\xi);z,y] \equiv \delta(x-y)$$$$ for any $$h(\xi)$$. Then one can obtain: $$$$\dfrac{\delta}{\delta{h(z)}}F[h(\zeta);x,y] = -\int d\xi d\eta F[h(\zeta);x,\xi]\dfrac{\delta G[h(\zeta);\xi,\eta]}{\delta{h(z)}}F[h(\zeta);\eta,y]$$$$ Question:How can I prove/understand this functional derivative?