Partial Derivative Calculator

Use our free partial derivative calculator to compute ∂f/∂x, ∂f/∂y, and second-order partials for functions of x and y.

Math

Mode

f(x, y) =

x value

y value

Formula

Compute partial derivatives of functions f(x,y) using numerical central differences. Supports ∂f/∂x, ∂f/∂y, and second-order partials (∂²f/∂x², ∂²f/∂y², ∂²f/∂x∂y).

∂f/∂x = lim(h→0) [f(x+h,y)−f(x−h,y)]/(2h)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter f(x,y) using x and y variables.
2Enter the point (x₀, y₀).
3Select ∂f/∂x, ∂f/∂y, or second-order.
4Click Calculate.

Examples

f(x,y)=x²+y², ∂f/∂x at (1,2)

1.∂f/∂x = 2x = 2

Result: 2

Second-order partials

1.∂²f/∂x²=2, ∂²f/∂y²=2, ∂²f/∂x∂y=0

Result: 2

Frequently Asked Questions

The derivative of a multivariable function with respect to one variable, holding others constant.

x and y are supported as independent variables.

∂²f/∂x∂y uses central difference in both variables.

For smooth functions, ∂²f/∂x∂y = ∂²f/∂y∂x.

Any expression using x, y with sin, cos, exp, etc.

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CalculateMe Team

Last updated: 2026-07-14

Partial Derivative Calculator

Formula

How It Works

Examples

f(x,y)=x²+y², ∂f/∂x at (1,2)

Second-order partials

Frequently Asked Questions

What is a partial derivative?

What variables can I use?

How are mixed partials computed?

Clairaut's theorem?

What functions are supported?

Related Calculators

Partial Derivative Calculator

Formula

How It Works

Examples

f(x,y)=x²+y², ∂f/∂x at (1,2)

Second-order partials

Frequently Asked Questions

What is a partial derivative?

What variables can I use?

How are mixed partials computed?

Clairaut's theorem?

What functions are supported?

Related Calculators