Logarithmic Differentiation
What is the Formula of Logarithmic Differentiation?
Logarithmic Differentiation of a function f(x) is found by dividing the differentiation of the function by the function itself. i.e.
d/dx [log f(x)] = f ‘(x)/f(x)
Logarithmic differentiation of a function is calculated using the chain rule of differentiation. These functions are also used to solve exponential functions.
When Logarithmic Differentiation is used?
Logarithmic differentiation is used when one need to find the differentiation of the complex function, such as, multiplication or division of two fucntions, a function in power of another function, etc. Logarithmic differentiation solves such types of complex functions very easily.
What are the Examples of Log Differentiation?
Logarithmic differentiation is used to solve different functions, such as, exponential ecos x, product (x + 5)3 (x2 + 2)3, exponent (cos x)sin x , etc.
What are the Different Rules of Logarithmic Differentiation?
Logarithmic differentiation uses the following rules to obtain the differentiation of the complex functions, such as,
- Product Rule
- Quotient Rule
- Exponential Rule
Logarithmic Differentiation
Logarithmic Differentiation helps to find the derivatives of complicated functions, using the concept of logarithms. Sometimes finding the differentiation of the function is very tough but differentiating the logarithm of the same function is very easy, then in such cases, the logarithmic differentiation formula is used.
In calculus, the differentiation of some complex functions is found first by taking a log and then finding the logarithmic derivative of that function.
In this article, we will learn about Logarithmic Differentiation in detail.
Table of Content
- What is Logarithmic Differentiation?
- Logarithmic Differentiation Formula
- Derivation of Logarithmic Differentiation Formula
- Applications of Log Differentiation
- Product of Functions (Product Rule)
- Division of Functions (Quotient Rule)
- Exponential Functions
- Method to Solve Logarithmic Functions
- Solved Examples on Logarithmic Differentiation
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