Let me give a short definition then make a question. Let $L$ be any smooth directional line on the XY plane. That is ,for any point $p$ on $L$ , just one tangent line exists. Let the tangent spin speed at $p$ on $L$ be defined as the limit of $function1$ at $p$ when a point $q$ approaches to $p$ along $L$ , against the direction of $L$. Where $function1$ is the ratio = $( tangent(q) - tangent(p) ) / (q.x - p.x)$ .
My question is this. Let $sL$ be an enough short segment of $L$. Where the tangent spin speed on $sL$ is known as constant $c$ ; and the initial tangent at the first end of $sL$ is known as $t$. Can you compute the derivative for $sL$? If yes , how?
Thank you in advance.
Please read the answer by user7530,it almost answers what I want. The remaining question follows. I said that the point $q$ moves along $L$ , but the tangent spin speed concerns the speed of $q$ only along the x-axis, not along $L$.