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I am very VERY confused!

Would anyone please be kind enough to point me in the right direction.

I read that, in general, the derivative of a tensor is not a tensor.

What do you find when you differentiate a tensor, then?

I thought that you wanted to find the acceleration, to find the curvature. Isn't the acceleration a vector and so a tensor?!

And if a vector is a rank 2 tensor, what is a 4-vector? Because when you differentiate those you get 4-vectors? 4-velocity and 4-acceleration?

I hope that makes sense, I'm getting more and more confused the more I read into it all.

Hannah