What is a good tool to make good looking mathematical animations?

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I want to make educational videos related to math and physics, I can handle the visuals of physics with Adobe AE, but the math part of it needs to be there too, so if anybody has some has some suggestions, please leave them.
What I want:

  • Good looking animations (Youtube)
  • The ability to graph functions, fully and partially (for ex, the arc of a circle, which increases over time), with the options of having a visible grid/axes (This one must be switchable for both, since there are times when there's no need for both, and times when both are needed)
  • The output should be in a common format (.mkv, .mp4, img sequence or something)