4 ms·
I've just been thinking of it as differentiation via integration. It took me until the end to realise that all I'd done was derive a form for the second deriva
by yarg 4y ago
I've just been thinking of it as differentiation via integration.
It took me until the end to realise that all I'd done was derive a form for the second derivative of F(x).
- goldenkey 4y agoAh 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.