What types of expressions are supported?

Polynomial expressions in x and y — terms with integer exponents and numeric coefficients. For example: 3x^2*y - 4xy^3 + 7x - 2y + 10. Trigonometric, exponential, and logarithmic functions are not supported.

How does partial differentiation work?

To take the partial derivative with respect to x, every term is differentiated using the power rule while y is treated as a constant. The exponent drops by 1 and the coefficient multiplies. Terms with no x become zero.

Can I enter expressions like 3x^2y or do I need the * sign?

Both forms are accepted. You can write 3x^2y, 3x^2*y, or 3*x^2*y — the parser normalises implied multiplication automatically.

Does the tool handle negative coefficients?

Yes. You can write expressions such as -2x^3 + 4xy - y^2 and the signs are preserved correctly throughout the computation.

What does it mean when a term differentiates to zero?

If a term contains none of the variable you are differentiating with respect to, it is a constant relative to that variable and its derivative is zero. Such terms are omitted from the result.

Partial Derivative Calculator

Name: Partial Derivative Calculator
Availability: InStock
Author: Nham Vu

Enter a multivariable polynomial and instantly compute its partial derivative with respect to x or y.

Enter Function f(x, y)

Polynomial expression

Supports integer exponents and numeric coefficients. Use ^ for powers.

Differentiate with respect to

x y

Quick examples

Result

Enter a function and click Compute to see the result.

Supported syntax

x^2 — x squared
3x^2*y or 3x^2y — implied multiplication
+ and - — add / subtract terms
Integer exponents only (negative exponents not supported)

Summary