  Scientific studies often require the precise calculation of derivatives. In
many cases an analytical calculation is not feasible and one resorts to
evaluating derivatives numerically. These are error-prone, especially for
higher-order derivatives. A technique based on algorithmic differentiation is
presented which allows for a precise calculation of higher-order derivatives.
The method can be widely applied even for the case of only numerically
solvable, implicit dependencies which totally hamper a semi-analytical
calculation of the derivatives. As a demonstration the method is applied to a
quantum field theoretical physical model. The results are compared with
standard numerical derivative methods.
