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.

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

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

Jul 23, 2025 · 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 the change in the …

Nov 16, 2022 · In this section we derive the formulas for the derivatives of the exponential and logarithm functions.

In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where f′ is the derivative of f. [1]

Since we know how to differentiate exponentials, we can use implicit differentiation to find the derivatives of ln(x) ln (x) and loga(x) log a (x). The videos below walk us through this process.

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) ln (x). As it turns out, the derivative of ln(x) ln (x) will allow us to …

Jun 3, 2025 · Compute the derivative of a logarithmic function, both natural-based and non-natural-based. Use logarithmic differentiation to determine the derivative of products and ratios of functions.

At first glance, taking this derivative appears rather complicated. However, by using the properties of logarithms prior to finding the derivative, we can make the problem much simpler.