$\dfrac{d}{dx}{\, \log_{e}{f{(x)}}}$ $\,=\,$ ${\dfrac{1}{f{(x)}}}{\dfrac{d}{dx}{\, f{(x)}}}$
The derivative of logarithm of a function is equal to the product of the reciprocal of the function and the derivative of the function.
$f{(x)}$ is a function in terms of $x$ and its natural logarithm is written as $\log_{e}{f{(x)}}$ or $\ln{f{(x)}}$. The differentiation of the natural logarithm of the function $f{(x)}$ with respect to $x$ is written mathematically as follows.
$\dfrac{d}{dx}{\, \log_{e}{[f{(x)}]}}$
The derivative of the natural logarithm of function $f{(x)}$ with respect to $x$ is equal to the product of the reciprocal of the function $f{(x)}$ and derivative of the function $f{(x)}$ with respect to $x$.
$\dfrac{d}{dx}{\, \ln{[f{(x)}}]}$ $\,=\,$ ${\dfrac{1}{f{(x)}}}{\dfrac{d}{dx}{\, f{(x)}}}$
The derivative rule for the natural logarithm of a function can be written in terms of any function and variable.
$(1) \,\,\,$ $\dfrac{d}{dm}{\, \log_{e}{g{(m)}}}$ $\,=\,$ ${\dfrac{1}{g{(m)}}}{\dfrac{d}{dm}{\, g{(m)}}}$
$(2) \,\,\,$ $\dfrac{d}{dp}{\, \log_{e}{r{(p)}}}$ $\,=\,$ ${\dfrac{1}{r{(p)}}}{\dfrac{d}{dp}{\, r{(p)}}}$
$(3) \,\,\,$ $\dfrac{d}{dz}{\, \log_{e}{s{(z)}}}$ $\,=\,$ ${\dfrac{1}{s{(z)}}}{\dfrac{d}{dz}{\, s{(z)}}}$
Learn how to derive the differentiation formula for the natural logarithm of a function.
List of solved problems to learn how to use the derivative of natural logarithm of a function formula in differential calculus.
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the maths problems in different methods with understandable steps.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved