The Partial Derivative Calculator is a valuable tool used in calculus to compute partial derivatives of functions with respect to specific variables. It assists in determining how a function changes concerning one variable while holding others constant.

## Formula of Partial Derivative Calculator

The formula for calculating the partial derivative with respect to a variable is represented as follows:

`∂f/∂x = lim (Δx → 0) [f(x + Δx, y) - f(x, y)] / Δx`

Where:

- ∂f/∂x is the partial derivative of the function f with respect to the variable x.
- f(x, y) is the original function.
- Δx is the change in the variable x.

Similarly, for the partial derivative with respect to y:

`∂f/∂y = lim (Δy → 0) [f(x, y + Δy) - f(x, y)] / Δy`

Where:

- ∂f/∂y is the partial derivative of the function f with respect to the variable y.
- f(x, y) is the original function.
- Δy is the change in the variable y.

## Table of General Terms:

Term | Description |
---|---|

Partial Derivative | The rate of change of a function concerning one of its variables while keeping others constant. |

Calculus | The branch of mathematics that deals with rates of change and accumulation. |

Function | A relation that assigns a unique output value to each input value. |

Variable | A symbol representing a quantity that can vary in a mathematical equation. |

## Example of Partial Derivative Calculator

Consider the function *f*(*x*,*y*)=*x*2+2*xy*+*y*2. We can use the Partial Derivative Calculator to find ∂f/∂x and ∂f/∂y.

**Calculation:**

- For ∂f/∂x:
- Substitute the function into the formula and compute the limit as Δx approaches 0.
- Determine the change in the function concerning x.

- For ∂f/∂y:
- Substitute the function into the formula and compute the limit as Δy approaches 0.
- Determine the change in the function concerning y.

## Most Common FAQs:

**What is the significance of****Partial Derivative**in real-life applications?Partial derivatives are crucial in various fields such as physics, economics, and engineering for analyzing rates of change and optimizing functions.

**How accurate are the results obtained from a Derivative Calculator?**The accuracy of the results depends on the precision of the calculator and the algorithm used for computation. However, for most practical purposes, the results are sufficiently accurate.

**Can the Partial Derivative Calculator handle complex functions?**Yes, the Partial Derivative Calculator can handle complex functions, provided the input is correctly formatted and the calculator’s capabilities are not exceeded.