Partial Derivative Calculator

Enter a function of several variables (use x, y, z …). Choose a variable for the partial derivative, or see the full gradient ∇f.

f(x, y, …)

Differentiate with respect to

∂f/∂x —

Gradient ∇f —

Frequently Asked Questions

What is a partial derivative?

A partial derivative measures how a multivariable function changes with respect to one variable while every other variable is held constant. For f(x, y) it is written ∂f/∂x or ∂f/∂y, and it is computed with the same differentiation rules as a single-variable derivative, treating the other variables as constants. For f = x²y, ∂f/∂x = 2xy and ∂f/∂y = x².

What is a gradient?

The gradient ∇f collects all of a function’s partial derivatives into one vector, one component per variable, so ∇f = (∂f/∂x, ∂f/∂y, …). It points in the direction of steepest increase of f at a given point, and its length gives the rate of that increase. For f = x² + y², the gradient is (2x, 2y).

How do I write a multivariable function here?

Use the letters x, y, z, w, t and similar single-letter names as variables, together with the functions sin, cos, tan, exp, ln and sqrt. Multiplication can use * or plain juxtaposition, so 2xy means 2·x·y, and powers appear in the usual exponent form, such as x²y or sin(xy). Parentheses group terms exactly as in ordinary algebra.

Is my data sent anywhere?

Your figures stay on your device when you use the partial derivative calculator. The partial derivative calculator works in the browser using JavaScript, with no server round-trip at any point, so your function is never transmitted. Nothing is logged, stored or shared with a third party. That also means the tool keeps working offline.

Partial Derivative Calculator

Frequently Asked Questions

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