Since the derivative of log x directly follows from the derivative of logₐ x, it is sufficient to prove the latter one. Let us prove this formula using different methods in the upcoming sections.

Generalising in another direction, the logarithmic derivative of a power (with constant real exponent) is the product of the exponent and the logarithmic derivative of the base: just as the logarithm of a …

May 24, 2024 · How to find the derivatives of natural and common logarithmic functions with rules, formula, proof, and examples.

Nov 16, 2022 · In this section we will discuss logarithmic differentiation. Logarithmic differentiation gives an alternative method for differentiating products and quotients (sometimes easier than using product …

Aug 21, 2025 · Derivative of log x is 1/x. The derivative of log x in calculus represents the rate of change of log x with respect to the change in the value of independent variable x.

Derivatives of logarithmic functions are mainly based on the chain rule. However, we can generalize it for any differentiable function with a logarithmic function.

Nov 14, 2025 · Use logarithmic differentiation to determine the derivative of a function. So far, we have learned how to differentiate a variety of functions, including trigonometric, inverse, and implicit …

The derivative of the logarithmic function is given by: f ' (x) = 1 / ( x ln (b) ) x is the function argument. b is the logarithm base. ln b is the natural logarithm of b. For example when: f (x) = log 2 (x) f ' (x) = 1 / …

We defined log functions as inverses of exponentials: \begin {eqnarray*} y = \ln (x) &\Longleftrightarrow & x = e^y \cr y = \log_a (x) & \Longleftrightarrow & x = a^y. \end {eqnarray*} Since we know how to …

In this section, we are going to look at the derivatives of logarithmic functions. We’ll start by considering the natural log function, ln(x). As it turns out, the derivative of ln(x) will allow us to differentiate not …