Understanding the Definition of the Derivative

Understanding the Definition of the Derivative

Understanding the Definition of the Derivative - In this video, I produce the definition of the derivative by thinking about slopes of tangent lines! I DO NOT use the definition of the derivative to actually calculate the derivative, although I have videos on that too!!

❤︎² Derivatives... What? (mathbff)

❤︎² Derivatives... What? (mathbff)

Nancy is on a new channel, NancyPi! New videos with Nancy will be at: https://youtube.com/NancyPi - MIT grad shows the DEFINITION of the derivative and how to FIND the derivative using that limit definition. To skip ahead: 1) For what the derivative MEANS, skip to 0:23. 2) For the SLOPE OF THE SECANT line, skip to 2:53. 3) For the SECANT BECOMING THE TANGENT and DEFINITION OF THE DERIVATIVE, skip to 5:54. 4) For how to FIND THE DERIVATIVE USING THE (LIMIT) DEFINITION of the derivative, skip to 10:28. For my video on the shorter, faster DERIVATIVE RULES to find the derivative, jump to: https://youtu.be/hCLfogkqzEk 1) WHAT IS THE DERIVATIVE? It's a function that tells you the slope (of the line tangent to the curve) at every point. Another way to think of it is that the derivative gives you the rate of change at any instant (the "instantaneous rate of change" at each point). You can find the derivative either with the proper DEFINITION OF THE DERIVATIVE ("by the limit process") or the faster, simpler way with the shortcut derivative rules such as the Power Rule, Product Rule, Quotient Rule, and Chain Rule. This video shows the first way, with the DEFINITION of the derivative, and how to use it to calculate the derivative. 2) SLOPE OF SECANT: To make the definition of the derivative, we can start with the slope of the straight secant line through a point x and some other point nearby, h distance away horizontally. If we label the two points and use the slope formula to write an expression for the slope of this secant line, the expression you get is [f(x+h) - f(x)] / h, which is also known as the DIFFERENCE QUOTIENT. 3) DEFINITION OF DERIVATIVE: That straight line slope we just found is actually a decent ESTIMATE for the slope at x, but it's not really the slope at x. We can get the EXACT slope of the tangent line at x by closing in on x and narrowing h to zero, by taking the LIMIT of the secant slope, as h approaches 0. The slope of the secant line becomes the slope of the tangent line. Not only is this limit equal to the slope of the tangent line, it is the definition of the derivative (when the limit exists) or f'(x). 4) FIND DERIVATIVE USING (LIMIT) DEFINITION: If you have to find the derivative "using the definition of the derivative" or "by the limit process", then you can use the limit definition we just found for any f(x) equation you're given. Remember that the f(x+h) part of the formula means to replace x with (x+h) anywhere x appears in the function f(x). If you want help knowing how to find the limit at the end, you can jump to my video "How to Find Any Limit": https://youtu.be/hewJikMkYFc

Finding a Derivative Using the Definition of a Derivative

Finding a Derivative Using the Definition of a Derivative

Buy my book!: '1001 Calculus Problems for Dummies' - you can get it on my website: http://patrickjmt.com/ Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a4f-91da-90841e168246&TDC_OfferCode=e2bf363b-0cb8-4635-98c3-2b5211d0847a&subject=math&grade=undefined for a FREE 30 minute session!Finding a Derivative Using the Definition of a Derivative - The long way! Two complete examples are shown. For more free math videos, visit http://PatrickJMT.com

What are Derivatives ?

What are Derivatives ?

An introduction to Derivatives.

Derivative as a concept

Derivative as a concept

Introduction to the idea of a derivative as instantaneous rate of change or the slope of the tangent line.

Calculus: Derivatives 1 | Taking derivatives | Differential Calculus | Khan Academy

Calculus: Derivatives 1 | Taking derivatives | Differential Calculus | Khan Academy

Finding the slope of a tangent line to a curve (the derivative). Introduction to Calculus. Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/calculus-derivatives-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus Missed the previous lesson? https://www.khanacademy.org/math/differential-calculus/taking-derivatives/derivative_intro/v/formal-and-alternate-form-of-the-derivative-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits. About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Differential Calculus channel: https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Explanation of a Derivative in Calculus : Calculus Explained

Explanation of a Derivative in Calculus : Calculus Explained

Subscribe Now: http://www.youtube.com/subscription_center?add_user=Ehow Watch More: http://www.youtube.com/Ehow Before you can work with derivatives in calculus you're going to need to know precisely what one is. Get an explanation of a derivative in calculus with help from an experienced math tutor in this free video clip. Expert: Ryan Malloy Filmmaker: Patrick Russell Series Description: Calculus is a more advanced mathematical topic than others, so feeling a little overwhelmed from time to time is only natural. Get an explanation for a wide variety of different calculus terms and situations with help from an experienced math tutor in this free video series.

Derivative Meaning

Derivative Meaning

Video shows what derivative means. Obtained by derivation; not radical, original, or fundamental.. Imitative of the work of someone else.. Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions.. derivative synonyms: spinoff, contingent claim, derived function. derivative pronunciation. How to pronounce, definition by Wiktionary dictionary. derivative meaning. Powered by MaryTTS

What is meaning of derivative and integration. By Ashish Surana,Surana Classes,Nashik(India)

What is meaning of derivative and integration. By Ashish Surana,Surana Classes,Nashik(India)

Basic concepts, what is practical use or physical significance of derivative and integration. Useful for all students from 11,12 (Science & commerce) and engineering diploma and degree. Lecture by 20 years experienced teacher Ashish Surana.BE (Electronics)

math animations derivatives

math animations   derivatives

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