Let $c:I\to\mathbb{R}$ a regular curve with curvature $k > 0, \forall t\in I$.
Then, $k(t)=\frac{||\dot{c}(t)\times\ddot{c}(t)||}{||\dot{c}(t)||^3}$, where $\dot{c}$ and $\ddot{c}$ are first and second derivative of function $c$.
Ok, so this is the context. Now, my proof starts with:
Let $s$ = natural parameter of curve. Then $\frac{dc}{dt} = \frac{dc}{dt}\frac{dt}{ds}$.
Let $h$ be the inverse function of $s$. So, $h(s)=t$. Then, $\frac{dc}{ds}(h(s))=\frac{dc}{dt}(h(s))\frac{dh}{ds}$ [...]
I am not familiar with Leibniz notation for derivatives. Can someone explain me why is the last statement true, and how it works?