Given the function $F(x+z,y+z)=0$,i need to find $dz$ and $d^2z$....here's my attempt:
$$dF=F'_1d(x+z)+F'_2d(y+z)=0$$ $$F'_1(x'dx+z'dz)+F'_2(y'dy+z'dz)=0$$ $$F'_1(dx+dz)+F'_2(dy+dz)=0$$ $$dz=-\frac{F'_1dx+F'_2dy}{F'_1+F'_2}$$ where $F'_1$ is derivative by first component,and $F'_2$ by second one.How can find $d^2z$ from the last equation?