Скачать или смотреть Calculus1 Lecture 16: The Chain Rule Differentiating Composite Functions

In this lecture, we introduce the Chain Rule, one of the most important tools for differentiating composite functions in Calculus.

Topics covered:

The Chain Rule theorem

Derivative of composite functions

Power of a function using the Chain Rule

Square–root and cube–root derivatives

Chain Rule with trigonometric functions

Differentiability of piecewise functions involving trigonometric expressions

Derivatives when angles are measured in degrees versus radians

Applications to function compositions

Chain Rule with intermediate variables

Several worked examples illustrate how the Chain Rule allows us to differentiate complex expressions by combining previously learned differentiation rules.

Instructor: Prof. Shadi Shaqaqha
Department of Mathematics – Yarmouk University

شرح قاعدة السلسلة (Chain Rule) لاشتقاق الدوال المركبة مع تطبيقات على الجذور والدوال المثلثية وتركيب الدوال.

00:00 The Chain Rule theorem
01:27 Basic example
03:26 Power of a function
05:00 Square-root and cube-root derivatives
07:31 Chain rule with trigonometric functions
09:20 Piecewise differentiability example
11:03 Degrees vs radians in trigonometric derivatives
15:08 Composition derivative example
14:12 Chain rule with intermediate variables