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.