Animating Newton Raphson Iteration using matplotlib

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I am trying to create this animation using Matplotlib animation features in Python. Unfortunately, I am not able to figure out what would be the driving logic for keeping the main curve intact and deleting the vertical and tangential lines.

I have made a very rudimentary try here and failing spectacularly since I am pretty new to the animation features of matplotlib (or for that matter any other package).

How can I build this animation?

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