Higher-Order Derivative in Parametric Form
We can also find higher order derivative of the function in the parametric form. Suppose we are given with functions y(t) and x(t) and they both are the function of parameter ‘t’. Then we can easily find the first order derivative as,
dy/dx = (dy/dt)×(dt/dx)
Now for finding the higher order derivative. Let dy/dt = y'(t) and dx/dt = x'(t) then,
d2y/dx2 = d/dx(dy/dx)
= {d/dt[(dy/dt)×(dt/dx)]}/dx/dt
= d/dt[y'(t)/x'(t)]×dt/dx
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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