{"id":3422,"date":"2024-06-24T16:36:18","date_gmt":"2024-06-24T16:36:18","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3422"},"modified":"2024-08-05T12:51:04","modified_gmt":"2024-08-05T12:51:04","slug":"the-chain-rule-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/chapter\/the-chain-rule-apply-it\/","title":{"raw":"The Chain Rule: Apply It","rendered":"The Chain Rule: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Explain and use the chain rule<\/li>\r\n\t<li>Use the chain rule along with other rules to differentiate functions involving powers, products, quotients, and trigonometry<\/li>\r\n\t<li>Use the chain rule to find derivatives when multiple functions are nested together<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Navigating the Chain Rule: Identifying and Applying Composite Function Derivatives<\/h2>\r\n<p>The chain rule is a fundamental concept in calculus that allows us to differentiate composite functions. In real-world applications, many complex functions are composed of simpler functions, making the chain rule an essential tool for solving a wide range of problems in physics, engineering, and economics. However, recognizing when to apply the chain rule and how to break down composite functions can be challenging. This apply-it task will help you develop your skills in identifying situations where the chain rule is necessary and guide you through the process of applying it to increasingly complex functions<\/p>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]287927[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]287928[\/ohm_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Explain and use the chain rule<\/li>\n<li>Use the chain rule along with other rules to differentiate functions involving powers, products, quotients, and trigonometry<\/li>\n<li>Use the chain rule to find derivatives when multiple functions are nested together<\/li>\n<\/ul>\n<\/section>\n<h2>Navigating the Chain Rule: Identifying and Applying Composite Function Derivatives<\/h2>\n<p>The chain rule is a fundamental concept in calculus that allows us to differentiate composite functions. In real-world applications, many complex functions are composed of simpler functions, making the chain rule an essential tool for solving a wide range of problems in physics, engineering, and economics. However, recognizing when to apply the chain rule and how to break down composite functions can be challenging. This apply-it task will help you develop your skills in identifying situations where the chain rule is necessary and guide you through the process of applying it to increasingly complex functions<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm287927\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=287927&theme=lumen&iframe_resize_id=ohm287927&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm287928\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=287928&theme=lumen&iframe_resize_id=ohm287928&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":15,"menu_order":13,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":560,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3422"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3422\/revisions"}],"predecessor-version":[{"id":4526,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3422\/revisions\/4526"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/560"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3422\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3422"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3422"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3422"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}