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 ...

This is a preview. Log in through your library . Abstract In this note we extend our previous results on the linear independence of values of the divided derivatives of exponential and quasi-periodic ...

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 ...

Often the time derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population’s growth rate is typically ...

Data from an experiment may result in a graph indicating exponential growth. This implies the formula of this growth is \(y = k{x^n}\), where \(k\) and \(n\) are constants. Using logarithms, we can ...

Simplify or manipulate expressions involving polynomial, radical, exponential, or logarithmic terms using appropriate properties and rules Use numeric or variable substitution while working with ...