{"id":155498,"date":"2022-03-26T00:42:46","date_gmt":"2022-03-25T19:12:46","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/product-rule-differentiation-rules-three-functions-and-formulas\/"},"modified":"2023-01-02T12:50:43","modified_gmt":"2023-01-02T07:20:43","slug":"product-rule-differentiation-rules-three-functions-and-formulas","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/","title":{"rendered":"Product Rule &#8211; Differentiation Rules, Three Functions and Formulas"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#What_is_Differentiation\" title=\"What is Differentiation?\">What is Differentiation?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#What_is_Derivative\" title=\"What is Derivative?\">What is Derivative?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#What_are_the_Differentiation_Rules\" title=\"What are the Differentiation Rules?\">What are the Differentiation Rules?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#We_are_Going_to_Discuss_Product_Rule_in_Detail\" title=\"We are Going to Discuss Product Rule in Detail\">We are Going to Discuss Product Rule in Detail<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#A_Few_Differentiation_Formulas_and_Examples_Have_Been_Listed_Below\" title=\"A Few Differentiation Formulas and Examples Have Been Listed Below:\">A Few Differentiation Formulas and Examples Have Been Listed Below:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#Product_Rule_for_the_Logarithms_to_Write_an_Equivalent_Sum_of_the_Logarithms\" title=\"Product Rule for the Logarithms to Write an Equivalent Sum of the Logarithms\">Product Rule for the Logarithms to Write an Equivalent Sum of the Logarithms<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Differentiation\"><\/span>What is Differentiation?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Differentiation is the process of mathematically finding the derivative of a function. The derivative is a measure of how a function changes as its input changes. It can be used to answer questions such as how fast a particular variable is growing or shrinking, or how a particular curve is changing.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155497 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/product-rule-differentiation-rules-three-functions-and-formulas.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/product-rule-differentiation-rules-three-functions-and-formulas.jpg?v=1648235562 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/product-rule-differentiation-rules-three-functions-and-formulas-300x212.jpg?v=1648235562 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Derivative\"><\/span>What is Derivative?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A derivative is a financial contract that derives its value from an underlying asset. The most common underlying assets are stocks, bonds, commodities, and currencies. Derivatives can be used for hedging (protecting against losses) or speculating (gambling on price changes).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_the_Differentiation_Rules\"><\/span>What are the Differentiation Rules?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three types of differentiation rules: product, quotient, and chain.<\/p>\n<p>The product rule states that the derivative of the product of two functions is the product of their derivatives.<\/p>\n<p>The quotient rule states that the derivative of the quotient of two functions is the quotient of their derivatives, divided by the the denominator of the quotient.<\/p>\n<p>The chain rule states that the derivative of the composition of two functions is the derivative of the first function, multiplied by the derivative of the second function, taken at the point where the first function is being applied.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"We_are_Going_to_Discuss_Product_Rule_in_Detail\"><\/span>We are Going to Discuss Product Rule in Detail<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The product rule is a mathematical theorem that states that the derivative of the product of two functions is the product of their derivatives. In symbols,<\/p>\n<p>This theorem is useful in calculating derivatives of composite functions.<\/p>\n<p>The product rule can be derived from the definition of the derivative of a function. Let<\/p>\n<p>be a function, and let<\/p>\n<p>and<\/p>\n<p>be two differentiable functions. Then, the derivative of<\/p>\n<p>is<\/p>\n<p>This follows from the definition of the derivative of a function, which is given by<\/p>\n<p>The derivative of a product is the product of the derivatives, so<\/p>\n<p>The proof of the product rule is a little more involved. First, note that<\/p>\n<p>This follows from the chain rule, which states that the derivative of the composite of two functions is the derivative of the first function multiplied by the derivative of the second function.<\/p>\n<p>Now, let<\/p>\n<p>be a function, and let<\/p>\n<p>and<\/p>\n<p>be two differentiable functions. Then, the derivative of<\/p>\n<p>is<\/p>\n<p>This follows from the product rule, since the derivative of a product is the product of the derivatives.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"A_Few_Differentiation_Formulas_and_Examples_Have_Been_Listed_Below\"><\/span>A Few Differentiation Formulas and Examples Have Been Listed Below:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>-Distance Formula: (Distance) = ( Rate x Time)<\/p>\n<p>-Area Formula: (Area) = (Base x Height)<\/p>\n<p>-Volume Formula: (Volume) = (Length x Width x Height)<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Product_Rule_for_the_Logarithms_to_Write_an_Equivalent_Sum_of_the_Logarithms\"><\/span>Product Rule for the Logarithms to Write an Equivalent Sum of the Logarithms<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The logarithm of a sum is the sum of the logarithms.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Differentiation? Differentiation is the process of mathematically finding the derivative of a function. The derivative is a measure [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Product Rule - Differentiation Rules","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"Learn about Product Rule topic of maths in details explained by subject experts on infinitylearn.com. Register free for online.","custom_permalink":"maths\/product-rule\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Product Rule - Differentiation Rules, Three Functions and Formulas<\/title>\n<meta name=\"description\" content=\"Learn about Product Rule topic of maths in details explained by subject experts on infinitylearn.com. Register free for online.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Product Rule - Differentiation Rules, Three Functions and Formulas\" \/>\n<meta property=\"og:description\" content=\"Learn about Product Rule topic of maths in details explained by subject experts on infinitylearn.com. Register free for online.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-25T19:12:46+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-01-02T07:20:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/product-rule-differentiation-rules-three-functions-and-formulas.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"vipin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Product Rule - Differentiation Rules, Three Functions and Formulas","description":"Learn about Product Rule topic of maths in details explained by subject experts on infinitylearn.com. Register free for online.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/","og_locale":"en_US","og_type":"article","og_title":"Product Rule - Differentiation Rules, Three Functions and Formulas","og_description":"Learn about Product Rule topic of maths in details explained by subject experts on infinitylearn.com. Register free for online.","og_url":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-03-25T19:12:46+00:00","article_modified_time":"2023-01-02T07:20:43+00:00","og_image":[{"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/product-rule-differentiation-rules-three-functions-and-formulas.jpg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"vipin","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#primaryimage","inLanguage":"en-US","url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/product-rule-differentiation-rules-three-functions-and-formulas.jpg?v=1648235562","contentUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/product-rule-differentiation-rules-three-functions-and-formulas.jpg?v=1648235562","width":606,"height":428},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/","name":"Product Rule - Differentiation Rules, Three Functions and Formulas","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"primaryImageOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#primaryimage"},"datePublished":"2022-03-25T19:12:46+00:00","dateModified":"2023-01-02T07:20:43+00:00","description":"Learn about Product Rule topic of maths in details explained by subject experts on infinitylearn.com. Register free for online.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Product Rule &#8211; Differentiation Rules, Three Functions and Formulas"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2"},"headline":"Product Rule &#8211; Differentiation Rules, Three Functions and Formulas","datePublished":"2022-03-25T19:12:46+00:00","dateModified":"2023-01-02T07:20:43+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#webpage"},"wordCount":445,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/product-rule\/#primaryimage"},"thumbnailUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/product-rule-differentiation-rules-three-functions-and-formulas.jpg","articleSection":["Maths"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2","name":"vipin","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","caption":"vipin"},"sameAs":["http:\/\/surge.infinitylearn.com"],"url":"https:\/\/infinitylearn.com\/surge\/author\/vipin\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/155498"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=155498"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/155498\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=155498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=155498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=155498"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=155498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}