{"id":153962,"date":"2022-03-25T23:00:21","date_gmt":"2022-03-25T17:30:21","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/logarithmic-differentiation-derivative-of-logarithm-and-formula\/"},"modified":"2022-12-22T15:33:00","modified_gmt":"2022-12-22T10:03:00","slug":"logarithmic-differentiation-derivative-of-logarithm-and-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/logarithmic-differentiation\/","title":{"rendered":"Logarithmic Differentiation &#8211; Derivative of Logarithm and Formula"},"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\/logarithmic-differentiation\/#Derivative_of_Logarithm\" title=\"Derivative of Logarithm\">Derivative of Logarithm<\/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\/logarithmic-differentiation\/#Function\" title=\"Function\">Function<\/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\/logarithmic-differentiation\/#Function_Derivative\" title=\"Function Derivative\">Function Derivative<\/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\/logarithmic-differentiation\/#Differentiation_in_y\" title=\"Differentiation in y\">Differentiation in y<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Derivative_of_Logarithm\"><\/span>Derivative of Logarithm<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The derivative of the <a href=\"https:\/\/infinitylearn.com\/surge\/blog\/iit-jee\/logarithmic-and-exponential-functions\/\">logarithm<\/a> function is the natural logarithm function. The derivative of the natural logarithm function is the logarithm function. Logarithmic Differentiation.<\/p>\n<p>In mathematics, the <b>logarithm<\/b> is the inverse function to exponentiation. That means the logarithm of a given number <span class=\"texhtml mvar\">x<\/span> is the <a class=\"mw-redirect\" title=\"Exponent\" href=\"https:\/\/en.wikipedia.org\/wiki\/Exponent\">expo<\/a>n<a class=\"mw-redirect\" title=\"Exponent\" href=\"https:\/\/en.wikipedia.org\/wiki\/Exponent\">ent<\/a> to which another fixed number, the <i>base<\/i> <span class=\"texhtml mvar\">b<\/span>, must be raised, to produce that number <span class=\"texhtml mvar\">x<\/span>. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. since <span class=\"texhtml\">1000 = 10\u2009\u00d7\u200910\u2009\u00d7\u200910 = 10<sup>3<\/sup><\/span>, the &#8220;logarithm base 10&#8221; of 1000 is 3, or <span class=\"texhtml\">log<sub>10<\/sub>\u2009(1000) = 3<\/span>. The logarithm of <span class=\"texhtml mvar\">x<\/span> to <i>base<\/i> <span class=\"texhtml mvar\">b<\/span> is denoted as <span class=\"texhtml\">log<sub><i>b<\/i><\/sub>\u2009(<i>x<\/i>)<\/span>, or without parentheses, <span class=\"texhtml\">log<sub><i>b<\/i><\/sub>\u2009<i>x<\/i><\/span>, or even without the explicit base, <span class=\"texhtml\">log\u2009<i>x<\/i><\/span>, when no confusion is possible, or when the base does not matter such as in big O notation.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-153961 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/logarithmic-differentiation-derivative-of-logarithm-and-formula.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/logarithmic-differentiation-derivative-of-logarithm-and-formula.jpg?v=1648229419 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/logarithmic-differentiation-derivative-of-logarithm-and-formula-300x212.jpg?v=1648229419 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Function\"><\/span>Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a <i>function<\/i> of time.<\/p>\n<p>Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).<\/p>\n<p>The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Function_Derivative\"><\/span>Function Derivative<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The derivative of a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Function_(mathematics)\">function<\/a> is a measure of how the function changes as its input changes. The derivative tells you how much the output of a function changes when the input changes by a small amount.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Differentiation_in_y\"><\/span>Differentiation in y<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>= sin(3x)<\/p>\n<p>The derivative of y = sin(3x) is y&#8217; = 3sin(3x). This is because the derivative of sin(x) is cos(x), and the derivative of 3x is 3.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Derivative of Logarithm The derivative of the logarithm function is the natural logarithm function. The derivative of the natural logarithm [&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":"Logarithmic Differentiation","_yoast_wpseo_title":"%%title%% %%page%% %%sep%%","_yoast_wpseo_metadesc":"Learn about logarithmic differentiation topic of maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/logarithmic-differentiation\/"},"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>Logarithmic Differentiation - Derivative of Logarithm and Formula -<\/title>\n<meta name=\"description\" content=\"Learn about logarithmic differentiation topic of maths in details explained by subject experts on infinitylearn.com.\" \/>\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\/logarithmic-differentiation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Logarithmic Differentiation - 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