Second Partial Derivative Calculator
Find fxx, fxy, and fyy for a quadratic two-variable function.
Calculator
What this calculator teaches
Second partial derivatives describe curvature in the x direction, y direction, and mixed direction.
They are the building blocks of the Hessian matrix used in optimization and surface analysis.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Second x partial | fxx = ∂²f/∂x² | Curvature when y is held constant. |
| Mixed partial | fxy = ∂²f/∂x∂y | How the x-slope changes as y changes. |
| Second y partial | fyy = ∂²f/∂y² | Curvature when x is held constant. |
Step-by-Step Examples
- fxx=2·2.
- fxy=3.
- fyy=2·4.
Where students use this
Common Mistakes to Avoid
Check denominator, domain, endpoint, and matrix-invertibility conditions before trusting a result.
Carry extra decimals through intermediate steps and round only the final answer.
Some topics need exact symbolic reasoning, while this calculator gives a clear numerical learning check.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This formula measures limiting behavior, instantaneous change, accumulation or multivariable variation. Assumption: The function must satisfy the continuity or differentiability conditions required by the method. Check domains, bounds, orientation and singularities.