Linear operators in calculus | Functions and mappings | Rates | Differential calculus | Mathematical analysis
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector. The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus relates antidifferentiation with integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus. (Wikipedia).
Calculus - What is a Derivative? (1 of 8) Overview
Visit http://ilectureonline.com for more math and science lectures! In this video I will give a general overview and the definition of “What is a derivative?”
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
Derivatives are the main object of study in differential calculus. They describe rates of change of functions. That makes them incredibly useful in all of science, as many models can be expressed by describing the changes over time (e.g. of physical quantities). However, the abstract defin
From playlist Summer of Math Exposition Youtube Videos
Definition of derivative in terms of a limit, (def 1)
Definition of derivative, calculus 1 homework solution. #calculus Check out my 100 derivatives: https://youtu.be/AegzQ_dip8k
From playlist Sect 2.7, Definition of Derivative
Calculus - What is a Derivative? (7 of 8) A Function Describing a Change (In a Function)
Visit http://ilectureonline.com for more math and science lectures! In this video I will describe the physical meaning of a derivative.
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
Calculus 1: What is a Derivative? (1 of 9) Basic Definitions
Visit http://ilectureonline.com for more math and science lectures! In this video I will introduce the basic definitions of what is a derivative. Next video in the series can be seen at: http://youtu.be/29Px0qXE1BU
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
definition of derivative for a rational function
Here we will use the definition of derivative to find the derivative of a rational function. This is a slightly harder calculus 1 problem so be sure you practice it a few times and make sure you can do it on your own. Get a derivative t-shirt: 👉 https://bit.ly/derivativetshirt Use "WELCO
From playlist Sect 2.7, Definition of Derivative
Calculus 3.03a - The Derived Function
The Derived Function, or better known as simply The Derivative. This is the beginning of the material on the definition of the derivative. The topic is approached in a fairly standard manner as the general case of the limit of a difference quotient.
From playlist Calculus Ch 3 - Derivatives
Calculus 2.8 The Derivative as a Function
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
derivative of x^-2 with the definition of derivative
We use the definition of derivative to find the derivative of x^-2. For more calculus tutorials, please see my new "just calculus" channel: 👉https://www.youtube.com/justcalculus If you find my videos helpful, then consider supporting me on Patreon: 👉 https://www.patreon.com/blackpenred
From playlist Sect 2.7, Definition of Derivative
Partial derivatives - How to solve?
► My Partial Derivatives course: https://www.kristakingmath.com/partial-derivatives-course Partial derivatives are just like regular derivatives, but for multivariable functions. We’re used to taking the derivative of a single variable function, which is simple because we just take the de
From playlist Calculus III
AP Calculus AB: Lesson 3.1 Elementary Derivative Rules
AP Calculus AB Unit 3: Derivative Rules Lesson 1: Elementary Derivative Rules
From playlist AP Calculus AB
MATH2018 Lecture 1.1. Partial Differentiation
We introduce partial derivatives, which allow us to calculate the rate of change of functions of several variables.
From playlist MATH2018 Engineering Mathematics 2D
Calculus AB Lesson 3.4 The Chain Rule
================================= AP Calculus AB / IB Math SL Unit 3: Derivative Rules Lesson 4: The Chain Rule =================================
From playlist AP Calculus AB
Derivatives for Beginners - Basic Introduction
This calculus video tutorial provides a basic introduction into derivatives for beginners. Here is a list of topics: My Website: https://www.video-tutor.net Patreon Donations: https://www.patreon.com/MathScienceTutor Amazon Store: https://www.amazon.com/shop/theorganicchemistrytutor
From playlist New Calculus Video Playlist
Worldwide Calculus: Higher-Order Derivatives
Lecture on 'Higher-Order Derivatives' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Derivatives of TRIG FUNCTIONS (KristaKingMath)
► My Derivatives course: https://www.kristakingmath.com/derivatives-course Each of the six trigonometric functions has a specific derivative. Trig functions are used so often in calculus that it's important to memorize the derivative for each of the six trig functions. With the derivativ
From playlist Calculus I
Calculus - What is a Derivative? (8 of 8) All the Different Notations of Derivatives
Visit http://ilectureonline.com for more math and science lectures! In this video I will describe and explain all the different notations of a derivative.
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
❖ Lots of Different Derivative Examples! ❖
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From playlist Calculus / First Semester - Limits, Continuity, Derivatives