If you’re currently studying the key equations which are used in the study of implicit differentiation, you’ve come to the right place. Simply continue reading a guide to understanding implicit differentiation as well as some of the most commonly used terms that you’ll come across in your study of implicit differentiation. An example of which is the term second differentiation.
What does the term implicit differentiation refer to?
The term implicit differentiation refers to a chain of rules which are used to work with derivatives. If you plan on studying or brushing up on your calculus skills, you’ll find that the bulk of exercises which you’ll work through feature y functions which are written as functions of x.
What is the d 2y dx 2 implicit differentiation?
Now that you’re aware of what implicit differentiation refers to, it’s time to learn about one of its key terms. Firstly, it’s important to understand what the equation above refers to. The equation d 2y dx 2 refers to what is referred to in mathematics as the second differentiation. If you’ve never heard of second differentiation, simply continue reading to find out more valuable information.
What exactly is the second differentiation and how is it used in mathematics?
The second differentiation is a method which you can use to figure out the nature of multiple of stationary points. Key examples of stationary points which you can figure out the nature of using implicit differentiation include maximum points, minimum points and points of inflection.
What are maximum points?
If you’re unsure about what the term maximum points refers to a circumstance when the gradient almost reaches its maximum point. In this scenario, just before the maximum point the gradient is positive and which is reaches its maximum it reaches zero. After the maximum point, the same gradient will be classed as being negative.
The term maximum point refers to the middle position where the gradient exactly reaches its maximum value.
What are minimum points?
Now that you fully understand what the term maximum points refers to, it’s time to learn about their counterparts which are called minimum points. Minimum points are positive and occur when a gradient has not met its maximum and has not reset to zero.
Remember that any gradient which reaches the maximum point or which surpasses the maximum point and become negative, is not an example of a minimum point.
What is an inflection point?
In order to better understand the process of using the second differentiation equation when dealing with implicit differentiation it’s also a wise idea to understand the term inflection point. What is an inflection point? An inflection point is any point which you can locate on a graph where a tangent successfully crosses a curve.
What does the term point of reflection refer to in mathematics?
The term point of reflection refers to a case where the derivative has reached a local maximum.
Why you should use a d 2y dx 2 calculator:
The quickest way to accurately calculate second differentiation problems is to use a calculator.
Hopefully you now have a clear understanding of implicit differentiation and its use in calculus.