{"id":35505,"date":"2022-09-28T12:04:41","date_gmt":"2022-09-28T04:04:41","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=35505"},"modified":"2026-06-08T14:23:07","modified_gmt":"2026-06-08T06:23:07","slug":"1-6-differentiation-chapter-2-rules-of-differentiation-2-1-rules-of-differentiation","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/calculus-i-academic-year-109-department-of-applied-mathematics-prof-cheng-fang-su\/1-6-differentiation-chapter-2-rules-of-differentiation-2-1-rules-of-differentiation","title":{"rendered":"1.6 Differentiation, Chapter 2 Rules of Differentiation, 2.1 Rules of Differentiation"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"35505\" class=\"elementor elementor-35505\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section 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class=\"elementor-heading-title elementor-size-default\">1.6 Differentiation, Chapter 2 Rules of Differentiation, 2.1 Rules of Differentiation\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7aec5b11 elementor-widget elementor-widget-video\" data-id=\"7aec5b11\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/xHazKMt1I20&quot;,&quot;modestbranding&quot;:&quot;yes&quot;,&quot;lazy_load&quot;:&quot;yes&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 *\/\n.elementor-widget-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video 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100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da19150 elementor-widget elementor-widget-shortcode\" data-id=\"da19150\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">\n<table id=\"tablepress-81\" class=\"tablepress tablepress-id-81\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Syllabus and Teaching Philosophy<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=29758&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Preliminaries and Notations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35463\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 1 Limits and Derivatives<br \/>\n1.1 Limits of Sequences<br \/>\n1.2 Limits of Functions <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35469\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.2 Limits of Functions<br \/>\n1.3 Evaluating Limits Analytically<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35475\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.3 Evaluating Limits Analytically<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35481\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.4 Continuous Functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35487\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.5 Limits at infinity; Asymptotes<br \/>\n1.6 Differentiation <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35493\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.6 Differentiation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35499\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.6 Differentiation<br \/>\n<br \/>\nChapter 2 Rules of Differentiation<br \/>\n2.1 Rules of Differentiation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35505\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.1 Rules of Differentiation<br \/>\n2.2 Chain Rule<br \/>\n2.3 Implicit Differentiation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35511\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.3 Implicit Differentiation<br \/>\n2.4 The Differentiation of the Inverse Functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35517\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.4 The Differentiation of the Inverse Functions<br \/>\n2.5 Differential and Linear Approximation<br \/>\n<br \/>\nChapter 3 Applications of Differentiation<br \/>\n3.1 Extreme Values on an Interval <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35523\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.1 Extreme Values on an Interval<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35529\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.2 The First Derivative Test<br \/>\n3.3 Concavity and the Second Derivative Test<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35535\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.3 Concavity and the Second Derivative Test<br \/>\n3.4 Summary of Curve Sketching <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35541\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.4 Summary of Curve Sketching<br \/>\n3.5 Rolle\u2019s Theorem and the Mean Value Theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35547\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.5 Rolle\u2019s Theorem and the Mean Value Theorem<br \/>\n3.6 Indeterminate Forms and L'Hospital\u2019s Rule<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35553\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.6 Indeterminate Forms and L'Hospital\u2019s Rule<br \/>\n3.7 Antiderivative<br \/>\n4.4 Indefinite Integrals<br \/>\n<br \/>\nChapter 5 Techniques of Integrals<br \/>\n(1)The Substitution Rule <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35559\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5 Techniques of Integrals<br \/>\n(1)The Substitution Rule<br \/>\n(2) Integration by Parts<br \/>\n(3) Trigonometric Integrals I <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35567\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5 Techniques of Integrals<br \/>\nReview of (1)-(3)<br \/>\n(4) Trigonometric Integrals II<br \/>\n(5) Trigonometric Substitution<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35575\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5 Techniques of Integrals<br \/>\n(5) Trigonometric Substitution<br \/>\n(6) Half-Angle Substitution<br \/>\n(7) Integration of Rational Functions by Partial Fractions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35581\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5 Techniques of Integrals <br \/>\n(7) Integration of Rational Functions by Partial Fractions <\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35587\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 4 Integration<br \/>\n4.1 Area<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35593\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.1 Area<br \/>\n4.2 Properties of Integrals<br \/>\n4.3 Fundamental Theorem of Calculus<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35599\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 5 Techniques of Integrals<br \/>\n(8) Improper Integrals<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35607\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 6 Applications of Integration<br \/>\n6.1 Area of a Region Between Two Curves<br \/>\n6.2 Volume<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35613\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">6.2 Volume <br \/>\n6.3 Arc Length<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35619\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.1 Curves Defined by Parametric Equations<br \/>\n7.2 Calculus with Parametric Curves<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35625\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.3 Polar Coordinates<br \/>\n7.4 Calculus with Parametric Curves<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35631\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Polar Curves<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35637\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Review<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35645\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Chapter 9 Vector and the Geometry of Space<br \/>\n9.1 Vectors in the Plane<br \/>\n9.2 Vectors in Space<br \/>\n9.3 The Dot Product of Two Vectors in Space<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=35651\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-81 from cache --><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-3 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-5f099062\" data-id=\"5f099062\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5b79cc32 elementor-widget-divider--view-line_text elementor-widget-divider--element-align-center elementor-widget elementor-widget-divider\" data-id=\"5b79cc32\" 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menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\">Contemporary 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href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-computer-science\" class=\"elementor-item\" tabindex=\"-1\">College of Computer Science<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5374\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biological-science-and-technology\" class=\"elementor-item\" tabindex=\"-1\">College of Engineering Bioscience<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5379\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-humanities-and-social-sciences\" class=\"elementor-item\" tabindex=\"-1\">College of Humanities Arts and Social Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5378\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-hakka-affair-culture\" class=\"elementor-item\" tabindex=\"-1\">College of Hakka Affair Culture<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118070\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-law\" class=\"elementor-item\" tabindex=\"-1\">School of Law<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\" tabindex=\"-1\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\" tabindex=\"-1\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\" tabindex=\"-1\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>1.6 Differenti&hellip;<\/p>\n","protected":false},"featured_media":0,"parent":29742,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","format":"standard","meta":{"footnotes":""},"categories":[1465],"tags":[],"class_list":["post-35505","course_page","type-course_page","status-publish","format-standard","hentry","category-calculus-i-a-109-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>1.6 Differentiation, Chapter 2 Rules of Differentiation, 2.1 Rules of Differentiation 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