Calculus1 Lecture 16: The Chain Rule Differentiating Composite Functions скачать в хорошем качестве

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