Partial Derivative Calculator
Compute partial derivatives of polynomial terms in x and y using the power rule.
Inputs
Enter function using x and y as variables.
Partial derivative
16.00000000
f(x, y)
10.00000000
Step by step
Values used
f(x, y) = x^2*y + 3*x*y^2 - 2*y; x value = 1; y value = 2; Differentiate with respect to = x
Partial derivative w.r.t. x
∂f/∂x ≈ [f(x+h, y) - f(x-h, y)] / (2h)
Partial derivative
= 16.00000000
f(x, y)
= 10.00000000
How it works
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)
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.