**ii)**Derive the following formulas of the Gaussian and Mean Curvature

$\displaystyle \overline{K}(F) = \frac{K}{J}$ where $\displaystyle J = (1-\varepsilon k_1)(1-\varepsilon k_2)$ and $\displaystyle k_i$ denote the principal vectors

Before I begin I managed to deduce from a previous problem that $\displaystyle (\overline{v})\times(\overline{w}) = J(p)v\times w$.

Now I would imagine that since $\displaystyle K=det(k_1,k_2)$ that I would simply have $\displaystyle F(k_1)\times F(k_2)$ wich would simply give $\displaystyle J(p)k_1 \times k_2$ which isn't the desired result.

So looking at both RHS and LHS I think I would get:

$\displaystyle F(k_1)\times F(k_2) = (k_1+\varepsilon k_1) \times (k_2+\varepsilon k_2)= k_1k_2(1-\varepsilon)^2$

then from the RHS I get :

$\displaystyle \frac{k_1k_2}{(1-\varepsilon k_1)(1-\varepsilon k_2)}$ which has lead nowhere.

I'm not looking for the answer, but any hints would be greatly appreciated.