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We obtain bounds for the complexity of circuit realisation of the system of differentials of orders from one to  k  of an arbitrary elementary function in terms of the circuit complexity of this function. Similar bounds are obtained for the complexities of realisation of the Jacobian and Hessian matrices. We point out some applications to deduction of bounds for complexities of polynomials in several variables, linear transformations, and quadratic forms.

On the complexity of calculation of differentials and gradients