Table of Contents
Derivative of Logarithm
The derivative of the logarithm function is the natural logarithm function. The derivative of the natural logarithm function is the logarithm function. Logarithmic Differentiation.
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. since 1000 = 10 × 10 × 10 = 103, the “logarithm base 10” of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation.
Function
Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.
Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.
Function Derivative
The derivative of a function is a measure of how the function changes as its input changes. The derivative tells you how much the output of a function changes when the input changes by a small amount.
Differentiation in y
= sin(3x)
The derivative of y = sin(3x) is y’ = 3sin(3x). This is because the derivative of sin(x) is cos(x), and the derivative of 3x is 3.
