{"id":635,"date":"2025-10-09T15:26:28","date_gmt":"2025-10-09T15:26:28","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus3\/?post_type=chapter&#038;p=635"},"modified":"2025-11-17T17:20:26","modified_gmt":"2025-11-17T17:20:26","slug":"advanced-partial-derivatives-get-stronger","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus3\/chapter\/advanced-partial-derivatives-get-stronger\/","title":{"raw":"Advanced Partial Derivatives: Get Stronger","rendered":"Advanced Partial Derivatives: Get Stronger"},"content":{"raw":"<h2>The Chain Rule<\/h2>\r\nThe problem set can be found using the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Calculus+3\/Problem+Sets\/Module+4\/The+Chain+Rule.pdf\">Problem Set: The Chain Rule<\/a> link. This link will open a PDF containing the problems for this section.\r\n<h2>Tangent Planes and Linear Approximations<\/h2>\r\nThe problem set can be found using the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Calculus+3\/Problem+Sets\/Module+4\/Tangent+Planes+and+Linear+Approximations.pdf\">Problem Set: Tangent Planes and Linear Approximations<\/a> link. This link will open a PDF containing the problems for this section.\r\n<h2>Directional Derivatives and the Gradient<\/h2>\r\nThe problem set can be found using the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Calculus+3\/Problem+Sets\/Module+4\/Directional+Derivatives+and+the+Gradient.pdf\">Problem Set: Directional Derivatives and the Gradient<\/a> link. This link will open a PDF containing the problems for this section.","rendered":"<h2>The Chain Rule<\/h2>\n<p>The problem set can be found using the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Calculus+3\/Problem+Sets\/Module+4\/The+Chain+Rule.pdf\">Problem Set: The Chain Rule<\/a> link. This link will open a PDF containing the problems for this section.<\/p>\n<h2>Tangent Planes and Linear Approximations<\/h2>\n<p>The problem set can be found using the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Calculus+3\/Problem+Sets\/Module+4\/Tangent+Planes+and+Linear+Approximations.pdf\">Problem Set: Tangent Planes and Linear Approximations<\/a> link. This link will open a PDF containing the problems for this section.<\/p>\n<h2>Directional Derivatives and the Gradient<\/h2>\n<p>The problem set can be found using the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Calculus+3\/Problem+Sets\/Module+4\/Directional+Derivatives+and+the+Gradient.pdf\">Problem Set: Directional Derivatives and the Gradient<\/a> link. This link will open a PDF containing the problems for this section.<\/p>\n","protected":false},"author":15,"menu_order":22,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-635","chapter","type-chapter","status-publish","hentry"],"part":428,"module-header":"practice","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\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/635","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":2,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/635\/revisions"}],"predecessor-version":[{"id":2316,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/635\/revisions\/2316"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/428"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/635\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=635"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=635"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=635"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=635"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}