Скачать или смотреть Calculus1 Lecture 19: Implicit Differentiation

In this lecture, we introduce implicit differentiation and explain how derivatives can be computed when a function is defined implicitly rather than explicitly.

Topics covered:

Explicit versus implicit functions

Implicit differentiation using the chain rule

Solving for
dy/dx
​
Implicit differentiation involving trigonometric functions

Second derivatives in implicit form

Tangent and normal lines to implicitly defined curves

Angles between curves

Intersection angles between a line and a curve

Angles of intersection between two circles

Several worked examples illustrate how implicit differentiation is applied to compute derivatives, find tangent lines, and determine angles between intersecting curves.

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

شرح الاشتقاق الضمني (Implicit Differentiation) وكيفية إيجاد المشتقة عندما تكون
y معرفة ضمنيًا، مع تطبيقات على المماس والزاوية بين المنحنيات.

00:20 Explicit vs implicit functions
01:01 Implicit differentiation procedure
01:50 Example 1 – Polynomial implicit equation
04:34 Example 2 – Trigonometric implicit equation
07:05 Example 3 – Second derivative implicitly
10:01 Tangent and normal lines
13:23 Angle between a line and a curve
19:05 Angle of intersection of two circles