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 ...

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 ...

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 ...

This is a preview. Log in through your library . Abstract In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein’s theorem for completely monotonic functions, some ...

A polynomial is an algebraic expression involving many terms and can be factorised using long division or synthetic division. Laws of logarithms and exponents Revise what logarithms are and how to use ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...