8Asymptotics for loss of stability
Automatic differentiation is a technique to compute the value f′(x0) of the derivative function f′ without knowing an explicit expression f′(x). The value is computed directly together with the function value f(x0) running through the formula tree of f(x). Thus one starts with x0 and constants c together with the derivatives 1 and 0 of x and c, respectively, and builds up f(x0) together with f′(x0), applying the corresponding rules for the differentiation. This technique should not be mixed up with symbolic differentiation, which can be found in algebra systems like MAPLE and which computes an expression f′(x) of f′ from that of f first and evaluates f′(x) at x0 afterwards. It also differs from numerical differentiation ...
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