Partial Derivative
If we have a function given as f(x, y) then its partial derivative is given with respect to x as ∂∮f(x, y)/∂x, and its partial derivative with respect to y is given as ∂f(x, y)/∂y.
- It should be noted that while partially differentiating a multivariable function with respect to a variable x then the variable ‘y’ in the function should be treated as constant and while partially differentiating the function with respect to y treat the variable ‘x’ as constant.
- For Example, if we have to find the partial differentiation of f(x, y) = x4y2 with respect to x and y then
- ∂f(x, y)/∂x = ∂(x4y2)/∂x = 4x3y2
- ∂f(x, y)/∂y = ∂(x4y2)/∂x = 2x4y
Derivatives | First and Second Order Derivatives, Formulas and Examples
Derivatives: In mathematics, a Derivative represents the rate at which a function changes as its input changes. It measures how a function’s output value moves as its input value nudges a little bit. This concept is a fundamental piece of calculus. It is used extensively across science, engineering, economics, and more to analyze changes.
Table of Content
- What are Derivatives?
- Derivatives Meaning
- Derivative by First Principle
- Types of Derivatives
- First Order Derivative
- Second Order Derivative
- nth Order Derivative
- Derivatives Formula
- Rules of Derivatives
- Derivative of Composite Function
- Chain Rule of Derivatives
- Derivative of Implicit Function
- Parametric Derivatives
- Higher Order Derivatives
- Partial Derivative
- Logarithmic Differentiation
- Applications of Derivatives
- Derivatives Examples
- Sample Problems on Derivatives
- Practice Problems on Derivatives
A derivative is a calculus tool that measures the sensitivity of a function’s output to its input. It is also known as the instantaneous rate of change of a function at a given position.
The derivative of a function with just one variable is the slope of the line that is tangent to the function’s graph for a given input value. In terms of geometry, the derivative of a function can be defined as the slope of its graph.
In this article we have covered Meaning of Derivatives along with types of derivatives, examples, formulas, applications and many more.
Contact Us