Partial Derivative Calculator (Multivariable)

Compute first-order and second-order partial derivatives (∂f/∂x, ∂f/∂y) and multivariable gradient vectors.

∂f / ∂x (treat y as constant)
6xy + 4y³ - 5
∂f / ∂y (treat x as constant)
3x² + 12xy² + 2
∂²f / ∂x²
6y
Mixed ∂²f / ∂x∂y (Clairaut's)
6x + 12y²

How to Use

  1. Enter the multivariable function f.
  2. Select First & Second Partial Derivatives to view the ∂f / ∂x (treat y as constant) and ∂f / ∂y (treat x as constant) and ∂²f / ∂x² and mixed ∂²f / ∂x∂y (clairaut's).