In this paper we derive the explicit, closed-form, recursion-free formulae for the arbitrary-order Fréchet derivatives of the exponential and logarithmic functions in unital Banach algebras (complex ...

In the Introduction to the Derivative video we introduce the notion of the derivative of a function and explain how the derivative captures the instantaneous rate of change of a function. In the ...

The derivatives for any functions like polynomial, power, exponential, logarithmic and circular functions can be easily found by knowing the derivative for their base function. For example, the ...

Founded in 1888, to further mathematical research and scholarship, the 30,000-member American Mathematical Society provides programs and services that promote mathematical research and its uses, ...

Abstract: This paper presents a rigorous mathematical analysis of the higher-order serial differentiator (HOSD), originally proposed by the authors for estimating time derivatives of time-varying ...

Concepts covered in this course include: standard functions and their graphs, limits, continuity, tangents, derivatives, the definite integral, and the fundamental theorem of calculus. Formulas for ...