1How to Learn from this Module…………………………………………………………………..2Icons of this Module.......................................................................................................................2What I Know (Pretest)…...............................................................................................................3Lesson 1:The Chain Rule...................................................................................................................5What’s In................................................................................................................5What’s New………………………………………………………………………………5What Is It................................................................................................................6What’s More..........................................................................................................8What I Have Learned...........................................................................................9What I Can Do.......................................................................................................9Lesson 2:ImplicitDifferentiation...............................................................................................10What’s In...............................................................................................................10What’s New………………………………………………………………………………..11What Is It...............................................................................................................11What’s More.........................................................................................................16What I Have Learned..........................................................................................17What I Can Do…………………………………………………………………………..18Lesson 3:Related Rates.....................................................................................................................19What’s In...............................................................................................................19What’s New………………………………………………………………………………. 19What Is It...............................................................................................................20What’s More………………………………………………………………………………22What I Have Learned..........................................................................................23What I Can Do......................................................................................................23Summary …………………………………………………………………………………………..24Assessment:(Posttest)……………………………………………………………………………27References.....................................................................................................................................29
1What This Module is AboutThis Module 3 of Basic Calculus presents the concepts of Chain Rule, Implicitdifferentiation and Related Rates which are basic and important applications of differentialcalculus. This module shows the concept of the chain rule, which states that thecomposition of functions is differentiable more formally stated as, if the functions f (x) andg (x) are both differentiable and defined.Besides illustrating on how to find the derivativeof a composite function, it also shows how to apply the chain rule correctly and facilitatescalculations that involve finding the derivatives of complex expressions, such as thosefound in many Physics applications.Further, this module 3 also presents and illustrates the fundamental rules of ImplicitDifferentiation and finally covers the concept of Related Rates. Furthermore, the moduleprovides sufficient examples with discussion and solutions, and exercises for students toself-assess their learning progress.Module ContentThe following are the lessons contained in this module:Lesson 1–The Chain RuleLesson 2–Implicit DifferentiationLesson 3–Related RatesWhat I Need to KnowAt the end of this module, you should be able to:1.illustrate the Chain Rule of differentiation.STEM_BC11Dlllh-22. Solve problems using Chain Rule.STEM_BC11DIIIh-13. Illustrate Implicit differentiation.STEM_BC11DIII-24. Solve problems (including logarithmic, and inverse trigonometric function) usingimplicit differentiation.STEM_BC11D - IIIj-15.Solve situational problems involving Related Rates.STEM_BC11D-IIIj-2
How to Learn from this ModuleTo achieve the objectives cited above, you are to do the following:•Take your time reading the lessons carefully.•Follow the directions and/or instructions in the activities and exercises diligently.•Answer all the given tests and exercises.Icons of this ModuleWhat I Need toThis part contains learning objectives thatKnoware set for you to learn as you go along themodule.What I knowThis is an assessment as to your level ofknowledge to the subject matter at hand,meant specifically to gauge prior relatedknowledgeWhat’s InThis part connects previous lesson with thatof the current one.
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