Derivative Calculator
Verified Calculation Engine
The online 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 derivative of a function: f'(x) = lim(h→0) [f(x+h) - f(x)]/h.
f'(x) = lim(h→0) [f(x+h) - f(x)]/h
Derivative represents rate of change or slope of tangent
Derivative is the instantaneous rate of change
Inputs
Results
Worked Examples
Example 1: Basic
Find derivative of f(x) = x² + 3x + 2
- function: x^2 + 3x + 2
- derivative: 2x + 3
- simplified: 2x + 3
Example 2: Board Level
Find derivative of f(x) = x³ - 5x² + 7x - 1
- function: x^3 - 5x^2 + 7x - 1
- derivative: 3x² - 10x + 7
- simplified: 3x² - 10x + 7
About this calculator
Overview
Derivative Calculator evaluates Derivative for the math / differentiation library. Primary input cue: Function f(x) [required]: Function expression. Method anchor: f'(x) = lim(h→0) [f(x+h) - f(x)]/h Derivative represents rate of change or slope of tangent. Derivative is the instantaneous rate of change.
When to use
Use Derivative Calculator when you already know the inputs and need derivative without setting up a spreadsheet.
Inputs explained
- Function f(x) [required]: Function expression
- Variable [optional]: Variable to differentiate with respect to (default: x)
Formula / method
f'(x) = lim(h→0) [f(x+h) - f(x)]/h Derivative represents rate of change or slope of tangent. Derivative is the instantaneous rate of change (calculator id: derivative-calculator).
Worked example
Worked values: function = x^2 + 3x + 2 → derivative = 2x + 3, simplified = 2x + 3
Interpreting results
Read the primary output as derivative under the method on this page.
Assumptions
- Units (when shown) must be consistent across inputs for derivative. [derivative-calculator]
- Empty required inputs are not silently replaced with zeros for derivative.
- Real-number arithmetic is used unless derivative explicitly needs integers.
Limitations
- This page does not provide a full textbook proof for every identity related to derivative.
- Derivative Calculator cannot invent missing inputs; incomplete forms stop short of a forged derivative value.
- Complex/branch cuts and undefined points are not always interactively annotated for 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
f'(x) = lim(h→0) [f(x+h) - f(x)]/h Derivative represents rate of change or slope of tangent. Derivative is the instantaneous rate of change (calculator id: derivative-calculator).
Example Calculation
Worked values: function = x^2 + 3x + 2 → derivative = 2x + 3, simplified = 2x + 3
Frequently Asked Questions
What is Derivative Calculator?
- Derivative Calculator evaluates Derivative for the math / differentiation library. Primary input cue: Function f(x) [required]: Function expression. Method anchor: f'(x) = lim(h→0) [f(x+h) - f(x)]/h Derivative represents rate of change or slope of tangent. Derivative is the instantaneous rate of change.
How does Derivative Calculator work?
- f'(x) = lim(h→0) [f(x+h) - f(x)]/h Derivative represents rate of change or slope of tangent. Derivative is the instantaneous rate of change (calculator id: derivative-calculator).
Why use this Math Numbers calculator?
- Use Derivative Calculator when you already know the inputs and need derivative without setting up a spreadsheet.