What are Logarithmic Functions?
The function that is the inverse of the exponential function is called the logarithmic function. It is represented as logbx, where b is the base of the log. The value of x is the value which equals the base of the logarithm raised to a fixed number y, thus, the general form of a logarithmic function is:
y = logbx
Where,
- y is the logarithm of x,
- b is the base of the logarithm, and
- x is the input of the logarithm.
Note: As we know, logarithms and exponentials are related to each other such that If y = logbx then, x = by.
Learn more about Logarithms.
Properties of Logarithmic Function
Some properties of the logarithmic function are listed below:
- log (XY) = log X + log Y
- log (X / Y) = log X – log Y
- log XY = Y log X
- log YX = ln X / ln Y
Read more about Log Rules.
Derivative of Logarithmic Functions in Calculus
Derivative or Differentiation of Logarithmic Function as the name suggests, explores the derivatives of log functions with respect to some variable. As we know, derivatives are the backbone of Calculus and help us solve various real-life problems. Derivatives of the log functions are used to solve various differentiation of complex functions involving logarithms. The differentiation of logarithmic functions makes the product, division, and exponential complex functions easier to solve.
This article deals with all the information needed to understand the Derivative of the Logarithmic Function in plenty of detail including all the necessary formulas, and properties. We will also learn about the problem with their solutions as well as FAQs and practice problems on Differentiation of Log functions.
Table of Content
- What are Logarithmic Functions?
- What is Derivative of Logarithmic Function?
- Derivative of Logarithmic Function Formula
- Proof of Derivative of Logarithmic Function Using First Principle
- Logarithmic Differentiation