directional derivatives for a composite function

Question

G $\in$ $C^1(R^2)$ with $G(1,1)-1\ge G(x,1)-x$ for all $x \in R$ and $G(1,1)\le G(1,y)$ for all $y \in R$

$F(s,t)=G(2st-s+1,2st+s+1)$. I've to found the directional derivative of F in $(0,0)$

respect the unit vector $v=(\sqrt{2}/2,\sqrt{2}/2)$

Answer 1

the directional derivative of F in (0,0) is: $lim_{t->0}$ ${G(t^2-{1\over \sqrt{2}}t+1,t^2+{1\over \sqrt{2}}t+1)-G(1,1)}\over t$ and then?