I found it like this: becuase \(\displaystyle \gamma\) is parametrize by arclength then \(\displaystyle \parallel T(s) \parallel =1, \forall s\), that means that \(\displaystyle T(s)\) can be written as \(\displaystyle T(s)=(cos \theta (s) , sin \theta (s))\), where \(\displaystyle \theta (s)\) is the angle beetwen \(\displaystyle T(s)\) and \(\displaystyle e_{1} = (1,0)\), then because \(\displaystyle \parallel T(s) \parallel =1\) we have that \(\displaystyle N(s)= \frac{ \dot{T(s)} }{\parallel \dot{T(s)} \parallel}\). we get \(\displaystyle k(s)=\langle \dot{T(s)} ,N(s) \rangle = \theta '(s)\) and we get the result we want.