Logarithmic Derivative Calculator
Verified Calculation Engine
The online Logarithmic Derivative Calculator helps you calculate instantly and solve problems related to Differentiation. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Finds derivatives of logarithmic functions: d/dx[ln(x)] = 1/x, d/dx[log_a(x)] = 1/(x ln(a)).
d/dx[ln(x)] = 1/x
d/dx[log_a(x)] = 1/(x ln(a))
d/dx[ln(f(x))] = f'(x)/f(x)
d/dx[log_a(f(x))] = f'(x)/(f(x) ln(a))
Derivatives of logarithmic functions
Inputs
Results
Worked Examples
Example 1: Basic
Find derivative of ln(x)
- function: ln(x)
- derivative: 1/x
- formula: d/dx[ln(x)] = 1/x
Example 2: Board Level
Find derivative of log(x)
- function: log(x)
- base: 10
- derivative: 1/(x ln(10))
- formula: d/dx[log₁₀(x)] = 1/(x ln(10))
About this calculator
Overview
Logarithmic Derivative Calculator evaluates Logarithmic Derivative for the math / differentiation library. Primary input cue: Logarithmic Function [required]: Function: ln(x), log(x), or log_a(x). Method anchor: d/dx[ln(x)] = 1/x d/dx[log_a(x)] = 1/(x ln(a)) d/dx[ln(f(x))] = f'(x)/f(x) d/dx[log_a(f(x))] = f'(x)/(f(x) ln(a)). Derivatives of logarithmic functions.
When to use
Appropriate when logarithmic derivative is the target quantity and the form fields match your known data.
Inputs explained
- Logarithmic Function [required]: Function: ln(x), log(x), or log_a(x)
- Base (Optional) [optional]: Base for log_a(x) (default: e for ln, 10 for log)
Formula / method
d/dx[ln(x)] = 1/x d/dx[log_a(x)] = 1/(x ln(a)) d/dx[ln(f(x))] = f'(x)/f(x) d/dx[log_a(f(x))] = f'(x)/(f(x) ln(a)). Derivatives of logarithmic functions (calculator id: logarithmic-derivative-calculator).
Worked example
Worked values: function = ln(x) → derivative = 1/x, formula = d/dx[ln(x)] = 1/x
Interpreting results
Read the primary output as logarithmic derivative under the method on this page.
Assumptions
- Empty required inputs are not silently replaced with zeros for logarithmic derivative. [logarithmic-derivative-calculator]
- Logarithmic Derivative is computed only from the fields you enter on this calculator.
- Real-number arithmetic is used unless logarithmic derivative explicitly needs integers.
Limitations
- If multiple conventions exist for logarithmic derivative, this calculator uses the convention implemented in its engine path.
- This page does not provide a full textbook proof for every identity related to logarithmic derivative.
- Complex/branch cuts and undefined points are not always interactively annotated for logarithmic derivative.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
d/dx[ln(x)] = 1/x d/dx[log_a(x)] = 1/(x ln(a)) d/dx[ln(f(x))] = f'(x)/f(x) d/dx[log_a(f(x))] = f'(x)/(f(x) ln(a)). Derivatives of logarithmic functions (calculator id: logarithmic-derivative-calculator).
Example Calculation
Worked values: function = ln(x) → derivative = 1/x, formula = d/dx[ln(x)] = 1/x
Frequently Asked Questions
What is Logarithmic Derivative Calculator?
- Logarithmic Derivative Calculator evaluates Logarithmic Derivative for the math / differentiation library. Primary input cue: Logarithmic Function [required]: Function: ln(x), log(x), or log_a(x). Method anchor: d/dx[ln(x)] = 1/x d/dx[log_a(x)] = 1/(x ln(a)) d/dx[ln(f(x))] = f'(x)/f(x) d/dx[log_a(f(x))] = f'(x)/(f(x) ln(a)). Derivatives of logarithmic functions.
How does Logarithmic Derivative Calculator work?
- d/dx[ln(x)] = 1/x d/dx[log_a(x)] = 1/(x ln(a)) d/dx[ln(f(x))] = f'(x)/f(x) d/dx[log_a(f(x))] = f'(x)/(f(x) ln(a)). Derivatives of logarithmic functions (calculator id: logarithmic-derivative-calculator).
Why use this Math Numbers calculator?
- Appropriate when logarithmic derivative is the target quantity and the form fields match your known data.