Chain rule, total differential

Using the chain-rule of partial differentiation (H, p 335) the total differential of (HT) can be obtained and isolated on the left hand of the equation Division of both sides of the resulting equation by dx yields a first order differential equation of the form... 

Given an some orbital- and eigenvalue-dependent xc-functional the main task is to derive a relation with allows the calculation of die xc potential (65). Two equivalent approaches to this task are possible. One can either minimize the total energy with respect to the total RKS potential under the subsidiary condition that the orbitals satisfy the RKS equations [48, 49,55,36] or one can use the chain rule for functional differentiation to replace the derivative with respect to 7 by derivatives with respect to and... 

To determine the defining ODE, we write the total differential of the family using the chain rule ... 

The ABPR approval does not affect the current EU total ban on the feeding of animal protein meals to farmed animals, which is a separate issue and remains in force until all the meat and bone meal in storage (approximately 400,000-500,000 tons) at present, awaiting incineration, does not hnd its way into the feed chain. The EU has also developed tests to differentiate the different types of animal protein meals. Such tests are needed in order to lift the ban for fishmeal and allow for traceability. However, the ABPR establishes clear safety rules for the production of meat and bone meal in case it is ever reauthorized for inclusion in feed for nonruminant species. Concurrent with the feed ban has been a ban against the export of animal protein meals. The United States was once the world s largest exporter with over a million tons exported per year now that figure is less than 300,000 tons (35). The timeline of the BSE situation follows ... 

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