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Calculus ADefinition Of The Derivative

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Syllabus
Videos

Elementary Transcendental Functions 143:02

Four Ways To Represent Function29:17
Mathematical Models19:35
New Functions From Old Functions22:16
Exponential Function26:33
Inverse Function And logarithms45:21

Limits and Continuity 132:07

Tangent And Velocity Problems18:22
The Limit Of A Function46:57
Continuity30:57
Infinite Limits35:51

The Derivative 168:34

Definition Of The Derivative14:15
Techniques Of Differentiation22:03
Derivatives of Trigonometric Functions23:30
Derivatives Of Logarithmic And Exponential Functions15:06
The Chain Rule21:23
Implicit Differentiation And Derivatives Of Inverse Trigonometric Functions11:55
Exponential Growth And Decay + Related Rates19:54
Linear Approximation And Differential18:08
Hyperbolic Functions22:20

Applications Of The Derivative 124:43

Extreme Values Of Function19:25
The Mean Value Theorem16:59
The First And The Second Derivative Tests29:42
Indeterminate Forms And L'Hospitals Rule16:03
Sketching The Graph Of The Function29:32
Minimization, Maximization And Optimization Problems13:02

Integrals 119:46

Areas And Distance Problem38:08
The Definite Integral25:10
The Fundamental Theorem Of Calculus08:55
Anti-Derivatives And Indefinite Integral+ Change Of variables in Indefinite Integration27:57
Area between curves19:36

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تعريف المشتقة هى نهاية f (a+h) – f(a) مقسومه على h عندما تؤؤل h الى الصفر.

ميل ال secant line عبارة عن التغير في ال y مقسوم على التغير في ال x اذن ميل المماس يساوى

وعند اخذ ال limit لميل ال secant line لكى نحصل على ميل المماس لمنحى الدالة او هنسميها مشتقة الدالة

مثال :

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