A derivative is a function which measures the slope. It depends upon x in some way, and is found by differentiating a function of the form y = f (x). When x is substituted into the derivative, the ...

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 ...

Graphs of exponential functions and logarithmic functions provide a visual insight into their properties, such as growth, decay, and the inverse relationship between them. Graphs of exponential ...

Exponential and logarithmic functions are mathematical concepts with wide-ranging applications. Exponential functions are commonly used to model phenomena such as population growth, the spread of ...

Abstract: The gradient matrix and its extensions have been useful tools in estimation theory [1], [3], [6]. Vetter developed the generalization to matrix-valued functions [4], [8]. Vetter's theory is ...

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 ...

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 ...