Partial Differentiation
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant.
For a multivariable function, like f(x, y) = x2y, computing partial derivatives looks something like this. Partial Derivative of f(x, y) w.r.t x is given by:
∂f/∂x = ∂(x2y)/∂x = 2xy, treating y as a constant
Partial Derivative of f(x, y) w.r.t y is given by:
∂f/∂y = ∂(x2y)/∂y = x2(1), treating x as a constant
The symbol ‘∂” is called as “del“, and it is used to distinguish partial derivatives from ordinary single-variable derivatives.
Related :
Differentiation
Differentiation in mathematics refers to the process of finding the derivative of a function, which involves determining the rate of change of a function with respect to its variables. It is a fundamental concept in calculus used to measure the function’s per unit change in the independent variable.
In this article, we will discuss the concept of Differentiation in detail including its definition, notations, various basic rules, and many many different formulas for differentiation.
Table of Content
- What is Differentiation in Calculus?
- Differentiation using First Principle
- Differentiation Rules
- Differentiation of Elementary Functions
- Differentiation Formulas
- Differentiation Techniques
- Higher Order Differentiation
- Partial Differentiation