Partial Derivative Calculator
Compute partial derivatives of polynomial terms in x and y using the power rule.
About Partial Derivative Calculator
Computes the partial derivative ∂f/∂x or ∂f/∂y numerically using central differences. When differentiating with respect to x, y is held constant and vice versa. Supports any expression in x and y that the parser can evaluate.
Formula
Partial derivative w.r.t. x
∂f/∂x ≈ [f(x+h, y) - f(x-h, y)] / (2h)
- f(x,y)
- Function of two variables
- h
- Step size (≈1e-7)
Worked example
With the default values below, Partial Derivative Calculator returns Partial derivative of 16.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x, y)
- x^2*y + 3*x*y^2 - 2*y
- x value
- 1
- y value
- 2
- Differentiate with respect toone of x, y
- x
Results
- Partial derivative
- 16.00000000
- f(x, y)
- 10.00000000
Step by step
- 1Values used
- 2Partial derivative w.r.t. x
- 3Partial derivative= 16.00000000
- 4f(x, y)= 10.00000000
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is a partial derivative?
It measures the rate of change of a multivariable function with respect to one variable while holding all others constant.
What functions can I enter?
Any expression using x and y with standard operations: +, -, *, /, ^, and functions like sin, cos, exp, ln, sqrt.