This tool calculates the second order partial derivatives of a given multivariable function to help you understand how the function curves in different directions.

## Second Order Partial Derivative Calculator

**How to use this calculator:**

- Enter your function f(x, y) in the function input field. Use ^ for powers, e.g., x^2 for (x^2).
- Enter the variables you’re differentiating with respect to, separated by a comma, in the variable input field (e.g., x, y).
- Specify the point (a, b) at which to evaluate the derivative, separated by a comma, in the point input field.
- Click the “Calculate” button and the second order partial derivative result will be displayed.

**How it calculates the results:**

This calculator uses a numerical approach to estimate the second order partial derivative using the central difference formula. It approximates the rate of change of the first derivative with respect to one variable, while holding the other variable constant at a particular point.

**Limitations:**

This calculator does not perform symbolic differentiation and is an approximation. Results for non-smooth functions, or at points where the derivative is not defined, may not be accurate. It does not check for discontinuities or points of nondifferentiability.