Partial Derivative Calculator
Calculate partial derivatives with nice formatting and simplification.
Syntax tip: Use * for multiplication (3*x, not 3x).
Derivative Result
Partial Derivatives, Solved Step by Step
Type any function of x, y, or z — like 3*x^2*y + 2*y^2 + 7*x — and this free calculator computes its first and second partial derivatives instantly, with the math typeset beautifully as you work.
Pick the variable to differentiate with respect to, and get clean, simplified results. Everything runs in your browser with the math.js engine, so answers appear the moment you click.
First and second derivatives
Compute ∂f/∂x, ∂f/∂y, and second-order partials like ∂²f/∂x² for any multivariable expression you enter.
Simplified, typeset output
Results are automatically simplified and rendered with MathJax, so the notation looks exactly like your textbook.
Free and private
The whole solver runs locally in your browser using the math.js library — your functions are never uploaded to a server.
How to use
- Type your function using * for multiplication (e.g. 3*x^2*y).
- Choose the variable to differentiate with respect to.
- Click Calculate and read the simplified partial derivatives.
Frequently Asked Questions
What is a partial derivative?
A partial derivative measures how a multivariable function changes when one variable changes while the others are held constant — written ∂f/∂x for the derivative with respect to x.
Can it compute second partial derivatives?
Yes. The tool computes second-order partials such as ∂²f/∂x² and mixed partials for the variables you choose.
What syntax should I use for the function?
Use * for multiplication (3*x, not 3x), ^ for powers (x^2), and standard function names like sin(x) and exp(x).
Is my input sent to a server?
No. All computation happens in your browser with the math.js library — nothing you type leaves your device.
Is the calculator free?
Yes, completely free with no signup or limits.
Related Math Tools
Check Out Other Popular Tools
Byte Converter
Convert between bits, bytes, KB, MB, GB, TB, and PB instantly. Supports binary (1024) and decimal (1000) conversion standards. Free data storage calculator.
Darken Image Online
Make an image darker instantly. Reduce brightness or add a dark overlay locally in your browser with 100% privacy.
Gen Z Slang Dictionary Test
How valid is your vibe? Test your knowledge of viral Gen Z slang, Brainrot terms, and internet culture. Get a Certified Vibe Check.
Was this tool helpful?
Comments
Loading comments...