These headlines tend to play (intentionally or unintentionally) on a misunderstanding of first and second order derivatives here.

Upstream interpolation is used to determine higher order derivatives.

A roof edge, is a discontinuity in the first order derivative of a grey-level profile.

Higher order derivatives can be similarly defined, leading to Newtonlike methods.

By extension, the higher order derivatives can be computed in a similar fashion.

Study of these higher order derivatives can improve approximations of the original displacement function.

The resulting system allowed the user to use automatically generated exact first and second order derivatives.

This is because the fundamental physical quantities involved within each of these examples are related through first and second order derivatives.

I am fairly clear of my position on this : ban all high order derivatives.

High order derivatives change the perceived risk profiles for bankers to the extent that they were able to sell nothing for something.