# How to find tangent at any point along a cubic hermite spline

I have a cubic hermite spline path that I am using to move sprites around on the screen (2D). I use two end points and two tangents to define the curve and then I use the basis functions for interpolation:

\begin{equation*} h_1(t) = 2t^3 - 3t^2 + 1\\ h_2(t) = -2t^3 + 3t^2\\ h_3(t) = t^3 - 2t^2 + t\\ h_4(t) = t^3 - t^2 \end{equation*}

What I want to do is have my sprite point in the direction of the curve as it is traveling along it. As I understand it from searching, the tangent to the curve (which I am assuming is the direction I want my sprite to face) involves taking the derivative of the function, however my calculus is severely lacking and once I do have the derivative, what do I do with it? Will it give me a new set of basis functions where I can just plug in a time t and get the tangent at that location?

$h'_1(t)=6t^2-6t$
$h'_2(t)=-6t^2+6t$
$h'_3(t)=3t^2-4t+1$
$h'_4(t)=3t^2-2t$