Higher Order Derivatives | Calculus Lesson 15 - JK Math

How to Find Higher-Order Derivatives (Calculus Lesson 15)

In this lesson we learn about higher-order derivatives. If you take the derivative of a derivative, you end up with the second derivative, which is a higher-order derivative. The derivative of the second derivative would be the third derivative, and so on. We discuss first, second, third, fourth, and nth derivatives of functions along with each of their notations. We then look at examples of taking several derivatives of the same function to find these higher order derivatives. We also revisit our rates of change from lesson 11 and discuss how the second derivative of the position function is the acceleration function.

This course is designed to help students understand the concepts of calculus at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with each lesson under 20 minutes!

Calculus requires a solid understanding of precalculus and algebra concepts and techniques including factoring, equation manipulation, trigonometric equations, logarithms, finding slope, graphing, and many more. If you are not familiar with these prerequisite topics, be sure to learn them first!

Video Chapters:
0:00 What are Higher Order Derivatives?
1:31 Notation for Higher Order Derivatives
3:13 Example 1 - Fourth Derivative of 2x^6+3x^3-4x^2+12x-5
6:14 Example 2 - Second Derivative of 8x^(3/2)
7:41 Example 3 - Second Derivative of 3x*sin(x)
10:01 Applying Higher Order Derivatives to Rates of Change
11:12 Example 4 - Finding the Acceleration Function

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