Chain rule applied in one point

Question

Let $g(u, v)=e^u + \sin v$ and $f(x, y, z)=(xy, xz)$ . Calculate $D(g o f)$ in $(0,1,0)$ applying chain rule. So here is what I have done: $$\frac{\partial g}{\partial x} = \frac{\partial g1}{\partial u} \frac{\partial u}{\partial x} + \frac{\partial g2}{\partial u} \frac{\partial u}{\partial x} = e^u * y + 1*y + \cos v * z $$ $$\frac{\partial g}{\partial y} = \frac{\partial g1}{\partial u} \frac{\partial u}{\partial y} + \frac{\partial g2}{\partial u} \frac{\partial u}{\partial y} = e^u * x + u*y $$ $$\frac{\partial g}{\partial z} = \frac{\partial g2}{\partial v} \frac{\partial v}{\partial z} = \cos v * x $$ I think I am going in a good way but I do not know what I should do now.