I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from?

Thanks!

a derivative is a rate of change. As speed is the rate of change of distance.

http://www.themathpage.com/aCalc/derivative.htm

Of course! I'd be happy to help you understand derivatives in calculus.

A derivative represents the rate at which a function is changing at any given point. In the context of instantaneous speed, a derivative measures the rate at which the position of an object is changing at a specific moment in time.

To understand derivatives better, it's important to start with the concept of a limit. The derivative of a function can be thought of as the limit of the average rates of change of the function as the interval over which the change is measured approaches zero. In simpler terms, it measures the slope of the function at a specific point.

To calculate a derivative, calculus provides various techniques such as the Power Rule, Product Rule, Quotient Rule, and Chain Rule. These rules allow you to find the derivative of a function by manipulating its algebraic expression.

To learn more about derivatives and improve your understanding, I recommend checking out the following resources:

1. Khan Academy: This website offers a comprehensive course on calculus, including specific lessons on derivatives and their applications. You can find detailed explanations, examples, and practice problems. Here's the link to their calculus course: https://www.khanacademy.org/math/calculus-1

2. Paul's Online Math Notes: This website provides free, easy-to-follow notes on various mathematical topics, including calculus. Their section on derivatives explains the basics and provides step-by-step examples. Here's the link to their derivative notes: http://tutorial.math.lamar.edu/Classes/CalcI/DiffIntro.aspx

3. YouTube Tutorials: There are plenty of educational videos available on YouTube that explain derivatives conceptually and demonstrate how to calculate them. Some popular channels to explore include 3Blue1Brown, Math Antics, and PatrickJMT.

Remember, understanding derivatives is a gradual process, so don't hesitate to practice and ask questions as you go along. Good luck with your studies, and feel free to ask if you have any further questions!