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This paper presents a new approach to Automatic Differentiation (AD) for a scalar valued and twice continuously differentiable function f : R^n - R. A new arithmetic is obtained based on the chain rule and using augmented algebra of real numbers. The chain rule based differentiation arithmetic is used to find the Gradient and Hessian. Jacobian is evaluated using Gradient arithmetic by computing Gradient for components and is arranged in matrix form to give Jacobian value. The resulting derivative evaluation uses the operator overloading concept which uses computer programs written in C++

Derivation of Augmented Arithmetic for Computing Gradient, Hessian and Jacobian through Forward Mode AD Using Dual Numbers