Like what you saw?
Create FREE Account and:
- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics
Derivative Notation - Concept
PhD. in Mathematics
Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.
The two commonly used ways of writing the derivative are Newton's notation and Liebniz's notation. Newton's notation involves a prime after the function to be derived, while Liebniz's notation utilizes a d over dx in front of the function. These two methods of derivative notation are the most widely used methods to signify the derivative function.
I want to talk about derivative notation, there are two main forms of derivative notation, there's the Newton form and the Leibniz form. These two forms are named for the two co creators of Calculus. Now the Newton form is the one we've been using so far it's the so called prime form. Now let's suppose we have a function f of x, the Newton form of derivative is f prime of x. If we have a function y like y equals x squared we would say its derivative is y prime. And if we wanted to talk about just the expression, x squared plus 1 you could write x squared plus 1 in parenthesis prime and all of these mean the derivative.
But Leibniz form works a little differently, there is this notation here d over dx this is called the differential operator and what it basically means is the derivative with respect to x of f of x or the derivative with respect to x of y or the derivative with respect to x of x squared plus 1. What's great about this is you see the operation of differentiation with Leibniz form and it has a little shorter version when you have the derivative with respect to x of y you can write that dy dx and this is something you'll see a lot of or df dx you'll occasionally see.
Now one of the things that this highlights is that differentiation or the derivative is an operation that you perform on a function. And I want to highlight the difference between the derivative of a function and the process of differentiation. Differentiation is the process of getting the derivative. So let's imagine that here's a function and this is the differentiation machine the process of getting the derivative. The result is the actual derivative, so remember that differentiation is the process you differentiate a function and the result is the derivative f prime of x.
Stuck on a Math Problem?
Ask Genie for a step-by-step solution
Please enter your name.
Are you sure you want to delete this comment?
- Instantaneous Rate of Change 22,836 views
- The Definition of the Derivative 22,546 views
- The Derivative Function 15,857 views
- Derivatives of Linear Functions 16,310 views
- Derivatives of Power Functions 19,355 views
- Derivatives of Polynomial Functions 14,366 views
- An Important Limit 10,741 views
- Derivatives of Exponential Functions 14,674 views
- Derivatives of Logarithmic Functions 15,374 views
- Average Velocity 26,892 views
- Average Rate of Change 22,072 views
- Instantaneous Velocity 23,537 views