Advanced Partial Derivative Calculator
Calculate partial derivatives for multivariable functions with detailed step-by-step solutions. Professional-grade mathematical tool with advanced features.
Function Input
Enter a mathematical function and select the variable to differentiate with respect to. Supports common mathematical operations and functions.
Partial Derivative Result
Step-by-Step Solution
Evaluate at Point
Common Examples
Simple Polynomial
Function: x² + y²
∂/∂x = 2x
Trigonometric
Function: sin(x)cos(y)
∂/∂x = cos(x)cos(y)
Three Variables
Function: xyz
∂/∂y = xz
Exponential & Log
Function: eˣ + ln(y)
∂/∂x = eˣ
Mixed Terms
Function: x³ + 3xy²
∂/∂x = 3x² + 3y²
Complex Expression
Function: x²y + y²z + z²x
∂/∂z = y² + 2zx
Frequently Asked Questions
What is a partial derivative?
A partial derivative measures how a function changes when one variable changes while keeping all other variables constant. It’s denoted as ∂f/∂x for the partial derivative of function f with respect to variable x.
What functions are supported?
Our calculator supports polynomials, trigonometric functions (sin, cos, tan), exponential functions (exp), logarithmic functions (ln), and combinations of these with basic arithmetic operations (+, -, *, /, ^).
How do I enter a function?
Use standard mathematical notation: x^2 for x squared, sin(x) for sine of x, exp(x) for e^x, ln(x) for natural logarithm. Variables can be x, y, z, t, u, or v.
Can I save my calculations?
Yes! The calculator automatically saves your calculation history in your browser. You can access it anytime by clicking the History button.
Is this calculator free to use?
Absolutely! Our partial derivative calculator is completely free to use with no registration required. Use it for homework, research, or professional work.
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