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Ah yes, this is why epsilon squared equals 0 in the dual numbers -- to automatically remove all higher order derivatives when they appear. Exponents on derivati
by goldenkey 4y ago
Ah yes, this is why epsilon squared equals 0 in the dual numbers -- to automatically remove all higher order derivatives when they appear. Exponents on derivatives are indicate of their rank/order.
- yarg 4y agoIt's the second symmetric derivative. https://en.wikipedia.org/wiki/Symmetric_derivative#The_second_symmetric_derivative https://en.wikipedia.org/wiki/Symmetric_derivative#The_secon... https://en.wikipedia.org/wiki/Second_derivative#Limit https://en.wikipedia.org/wiki/Second_derivative#Limit > The limit is called the second symmetric derivative. Note that the second symmetric derivative may exist even when the (usual) second derivative does not. > This limit can be viewed as a continuous version of the second difference for sequences. So it actually can do what I intended it to do, nothing original - but there was a degree of satisfaction in deriving it myself.
- goldenkey 4y agoThanks yarg, I just learned something new.