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Step-by-step calculus

Partial Derivative Calculator

Differentiate multivariable functions with respect to a selected variable while holding the other independent variables constant.

Works in your browserSteps explainedVideo explanations

Learn the method

Choose what changes and what stays fixed

A partial derivative measures change along one variable while other independent variables stay constant.

f(x,y)=x2y+sin⁡(xy),fx=2xy+ycos⁡(xy)f(x,y)=x^2y+\sin(xy),\qquad f_x=2xy+y\cos(xy)
Calculus formulas

Worked example

  1. 1Choose x as the differentiation variable; hold y constant.
  2. 2The partial derivative of x²y is 2xy.
  3. 3The chain rule gives ∂sin(xy)/∂x=y cos(xy). Add the terms.

This differs from implicit differentiation, where y depends on x. A repeated partial differentiates again with respect to the selected variable; specify a sequence for mixed partials.

What this partial derivative calculator does

  • Select the variable to differentiate and keep others constant.
  • Find first and repeated partial derivatives.
  • Request mixed partial derivatives explicitly in the problem statement.
  • No automatic one-variable numeric verification is claimed for multivariable results.

How to use it

  1. Enter a function or equation, or use the formula keyboard or a photo.
  2. Check the variable and differentiation settings, then press Solve.
  3. Read the steps, ask a follow-up question, or create a video lesson from the result.

Questions about the partial derivative calculator

Are mixed partial derivatives always equal?

Not always. Continuity of the second partial derivatives in a neighborhood is a sufficient condition for equality. Specify the order and check the assumptions.

Does this calculator show steps?

Yes. The solver explains the rules and intermediate expressions. AI can make mistakes; check the assumptions and each step.

Can I generate a video explanation?

After solving, choose Video lesson to generate a narrated whiteboard explanation. Generation is subject to the displayed quota.