Higher-Order Derivatives
What is Derivative of a Function?
The derivative of a function is defined as the instantaneus rate of change of a function at any given point. The slope of any curve is also defined using the derivative of the function.
What does First Order Derivative of a Function denotes?
First order derivaties of a function gives the instantaneous rate of change of the function at any given point. The first order derivative of a function is given using the first principle.
What does Second Order Derivative of a Function denotes?
Second order derivative of a function is given when we differentiate the first order derivative of the function if the first order derivative of the function is a differentiable function.
What is Equation for Derivative of the First Order in Parametric Form?
Equation for Derivative of the First Order in Parametric Form is, dy/dx = (dy/dt) × (dt/dx) where t is the parameter
What is Equation for Derivative of the Second Order in Parametric Form?
Equation for Derivative of the Second Order in Parametric Form is, d2y/dx2 = (d/dx) (dy/dx) = (d/dt)((dy/dt) × (dt/dx))× (dt/dx) where t is the parameter
Higher Order Derivatives
Higher Order Derivatives are the second, third, or further derivative of the function, i.e. differentiating a function multiple times results in a higher order derivative. Suppose we have a function f(x) then its differentiation is f'(x) which is a first-order derivative. Then its differentiation again f”(x) is called the second order derivative. This is the Higher Order Derivative and then differentiating the second order derivative again results in the third order derivative i.e. f”'(x) is the third derivative of the function f(x) and then higher derivatives are further calculated.
These Higher Order Derivatives are used for various purposes they are used to find the maxima and minima of the function, it is also used for finding the optimal solution of a function, etc.
In this article, we will learn about, Higher Order Derivatives definition, Second Order derivative, Third Order derivative, examples, and others in detail.
Table of Content
- Higher Order Derivatives Definition
- Second Order Derivatives
- Third Order Derivative
- Higher-Order Derivative in Parametric Form
- Application of Higher Order Derivative
- Examples
- FAQs
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