What is Derivative of Natural log x?
Derivative of Natural log x is 1/x. It implies that change in the value of log x with respect to change in the input variable, i.e. x is 1/x. Also, it defines the slope of the tangent to the curve represented by y = log x, at any point x = x1. The formula for derivative of natural log x is written as follows:.
Derivative of Natural log x Formula
d/dx [log x] = 1/x
or
(log x)’ = 1/x
The derivation for this formula using the first principle of differentiation and implicit differentiation is discussed as follows.
Derivative of ln x (Natural Log)
The derivative of ln x is 1/x. We can also say that the derivative of natural log x is 1/x. The derivative of any function gives the change in the functional value with respect to change in the input variable. Natural log x is an abbreviation for the logarithmic function with the base as Euler’s Number, i.e. e.
In this article, we will discuss the derivative of natural log x, various methods to derive it including the first principal method and implicit differentiation, some solved examples, and practice problems.