{"id":172427,"date":"2023-10-30T09:18:52","date_gmt":"2023-10-30T08:18:52","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=172427"},"modified":"2023-10-30T09:21:23","modified_gmt":"2023-10-30T08:21:23","slug":"demystifying-derivatives-understanding-the-core-of-calculus","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/demystifying-derivatives-understanding-the-core-of-calculus","title":{"rendered":"Demystifying Derivatives: Understanding the Core of Calculus"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"172427\" class=\"elementor elementor-172427\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5f87ba71 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5f87ba71\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-66a9fdad\" data-id=\"66a9fdad\" 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-59ede4cc elementor-widget elementor-widget-heading\" data-id=\"59ede4cc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">The notion of derivative is particularly used in DataScience for machine learning models. Apart from what you've probably seen in high school, the applications of this mathematical tool are much broader, and we'll come back to them at the end of this article.\nIn this article, you'll first learn how to calculate the derivative of a function, and then we'll look in a little more detail at the usefulness of this calculation.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2ef49bde elementor-widget elementor-widget-heading\" data-id=\"2ef49bde\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Definition<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-11eafa76 elementor-widget elementor-widget-text-editor\" data-id=\"11eafa76\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<blockquote><p><span style=\"color: #000000;\">The derivative of a function f(x) represents its rate of change. It may be denoted f'(x) or dfdx. Calculating and studying the derivative are important concepts in the study of functions.<br \/><\/span><\/p><\/blockquote>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5a8d990 elementor-widget elementor-widget-heading\" data-id=\"5a8d990\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Formulas<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6f2dbc57 elementor-widget elementor-widget-text-editor\" data-id=\"6f2dbc57\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Calculating a derivative is generally quite straightforward if you know the basic formulas for the usual functions.<\/p><p>These formulas are summarized in the table below:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7d3a677c elementor-widget elementor-widget-image\" data-id=\"7d3a677c\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"370\" height=\"512\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-7.png\" class=\"attachment-full size-full wp-image-172431\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-7.png 370w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-7-217x300.png 217w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-429e783f elementor-widget elementor-widget-text-editor\" data-id=\"429e783f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>This table gives you the most basic derivatives.<\/p><p><br \/>Sum of functions<\/p><p><br \/>If your function is the sum of several other functions :<\/p><p><br \/>f(x)=u(x)+v(x)<\/p><p><br \/>then its derivative will be the sum of the derivatives:<\/p><p><br \/>f'(x)=u'(x)+v'(x)<\/p><p><br \/>For example:<\/p><p><br \/>f(x)=x2+3<\/p><p><br \/>In this case u(x)=x2 and v(x)=3<\/p><p><br \/>We can therefore calculate<\/p><p><br \/>u'(x)=(x2)&#8217;=2&#215;2-1=2x<\/p><p><br \/>v'(x)=(3)&#8217; = 0<\/p><p><br \/>f'(x)=u'(x)+v'(x) = 2x + 0 = 2x<\/p><p><br \/>Products of functions<\/p><p><br \/>For multiplication of functions:<\/p><p><br \/>f(x)=u(x)*v(x)<\/p><p><br \/>The total derivative is a little more specific and follows the following rule:<\/p><p><br \/>f'(x)=u'(x)*v(x)+u(x)*v'(x)<\/p><p><br \/>f(x)=x2sin(x)<\/p><p><br \/>In this case u(x)=x2 and v(x)=sin(x)<\/p><p><br \/>We can therefore calculate<\/p><p><br \/>u'(x)=(x2)&#8217;=2&#215;2-1=2x<\/p><p><br \/>v'(x)=(sin(x))&#8217; = cos(x)<\/p><p><br \/>f'(x)=u'(x)*v(x)+u(x)*v'(x) = 2x*sin(x) + x2*cos(x)<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-57c2e07c elementor-widget elementor-widget-text-editor\" data-id=\"57c2e07c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Quotients of functions<\/p><p><br \/>Now if a function is the division of two other functions: f(x)=u(x)v(x) then the derivative will be<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7ceb9446 elementor-widget elementor-widget-image\" data-id=\"7ceb9446\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"70\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-2.png\" class=\"attachment-full size-full wp-image-172432\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-2.png 1024w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-2-300x21.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-2-768x53.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1f9731b3 elementor-widget elementor-widget-text-editor\" data-id=\"1f9731b3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Example :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4078b1c6 elementor-widget elementor-widget-image\" data-id=\"4078b1c6\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"70\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-3.png\" class=\"attachment-full size-full wp-image-172433\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-3.png 1024w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-3-300x21.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-3-768x53.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2033abc6 elementor-widget elementor-widget-text-editor\" data-id=\"2033abc6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>In this case u(x)=(3x+6) and v(x)=(x3-7)<\/p><p>We can therefore calculate<\/p><p>u'(x)=(3x+6)&#8217;=3<\/p><p>v'(x)=(x3-7)&#8217; =3&#215;2<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1d7612e1 elementor-widget elementor-widget-image\" data-id=\"1d7612e1\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"70\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-8-1.png\" class=\"attachment-full size-full wp-image-172434\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-8-1.png 1024w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-8-1-300x21.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Quotients-de-fonctions_equation-8-1-768x53.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5d41b3d elementor-widget elementor-widget-heading\" data-id=\"5d41b3d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Compound functions<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1be10877 elementor-widget elementor-widget-text-editor\" data-id=\"1be10877\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>If your function is perceived as two functions grouped together, or in other words, a function of a function:<\/p><p>h(x)=f(g(x))=f \u25e6 g<\/p><p>then its derivative is calculated as follows:<\/p><p>h'(x)=(f \u25e6 g) &#8216; = g&#8217; .(f &#8216; \u25e6 g)<\/p><p>For example:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-699c2bf2 elementor-widget elementor-widget-image\" data-id=\"699c2bf2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"55\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-3.png\" class=\"attachment-large size-large wp-image-172435\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-3.png 1025w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-3-300x20.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-3-768x52.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-59388bd2 elementor-widget elementor-widget-text-editor\" data-id=\"59388bd2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>We can therefore consider :<\/p><p>g(x)=x2+2x-4 and g'(x)=2x+2<\/p><p>f(x)=x and f'(x)=121&#215;1\/2=12x<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-74f46e7e elementor-widget elementor-widget-image\" data-id=\"74f46e7e\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"55\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-6.png\" class=\"attachment-large size-large wp-image-172436\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-6.png 1025w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-6-300x20.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-6-768x52.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-690f3eae elementor-widget elementor-widget-text-editor\" data-id=\"690f3eae\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">and<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5e10e4a7 elementor-widget elementor-widget-image\" data-id=\"5e10e4a7\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"55\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-7.png\" class=\"attachment-large size-large wp-image-172437\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-7.png 1025w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-7-300x20.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-7-768x52.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-65c89f3e elementor-widget elementor-widget-text-editor\" data-id=\"65c89f3e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">so<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2c3c2f68 elementor-widget elementor-widget-image\" data-id=\"2c3c2f68\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"55\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-8.png\" class=\"attachment-large size-large wp-image-172438\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-8.png 1025w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-8-300x20.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/Fonctions-composee_equation-8-768x52.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-202d9b6c elementor-widget elementor-widget-heading\" data-id=\"202d9b6c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Applications<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-75e1bcc8 elementor-widget elementor-widget-text-editor\" data-id=\"75e1bcc8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>But what&#8217;s the point of <strong>calculating the derivative?<\/strong><\/p><p>Simply put, the sign of the derivative indicates the variations of the function f. It represents the tangent to the function. And the derivative itself represents the directing coefficient of the tangent to f at the point.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5691cfd9 elementor-widget elementor-widget-image\" data-id=\"5691cfd9\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1029\" height=\"771\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-2-1.png\" class=\"attachment-full size-full wp-image-172439\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-2-1.png 1029w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-2-1-300x225.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-2-1-1024x767.png 1024w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-2-1-768x575.png 768w\" sizes=\"(max-width: 1029px) 100vw, 1029px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-53414101 elementor-widget elementor-widget-text-editor\" data-id=\"53414101\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Reminder: The tangent of a function at a point is the line that touches the function at that point, and only that point.<\/p><p>If f &#8216; \u2265 0, then f is increasing<\/p><p>If f &#8216; \u2264 0, then f is decreasing<\/p><p>And when f&#8217;=0, we have the point x for which the directing coefficient of the tangent cancels out, and the function f possibly changes variation.<\/p><p>For example<\/p><p>f(x)=x2-4x+2<\/p><p>f'(x)=2x-4<\/p><p>f'(x)=0 \u21d4 2x=4 \u21d4 x=2<\/p><p>This indicates that forx=2, my function may be changing its variation. As you can see below, x=2 is an inflection point:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-34716aa0 elementor-widget elementor-widget-image\" data-id=\"34716aa0\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1025\" height=\"782\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-3-1.png\" class=\"attachment-full size-full wp-image-172440\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-3-1.png 1025w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-3-1-300x229.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-3-1-768x586.png 768w\" sizes=\"(max-width: 1025px) 100vw, 1025px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21249e70 elementor-widget elementor-widget-text-editor\" data-id=\"21249e70\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>So, replacing x by x&lt;2 for example x=1,<\/p><p>We have:<\/p><p>f'(1)=2 \u00d7 1-4=\u23af2&lt;0<\/p><p>The derivative is less than 0, so the function f is decreasing.<\/p><p>Replacing x by x&gt;2 for example x=3,<\/p><p>we have :<\/p><p>f'(3)=2*3-4=2&gt;0<\/p><p>The derivative is greater than 0, so the function f is increasing.<\/p><p>We therefore have the following table of variation:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1400a6a4 elementor-widget elementor-widget-image\" data-id=\"1400a6a4\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1027\" height=\"493\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-8.png\" class=\"attachment-full size-full wp-image-172441\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-8.png 1027w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-8-300x144.png 300w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-8-1024x492.png 1024w, https:\/\/datascientest.com\/en\/files\/2023\/10\/unnamed-8-768x369.png 768w\" sizes=\"(max-width: 1027px) 100vw, 1027px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7f0c73f1 elementor-widget elementor-widget-text-editor\" data-id=\"7f0c73f1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><a href=\"https:\/\/datascientest.com\/en\/machine-learning-engineer-all-about-the-job\">So what does this have to do with Machine Learning?<\/a><\/p><p>In machine learning problems, we seek to find the minimum of the cost function in order to minimize the prediction error and thus maximize model performance.<br \/>To do this, we use the derivative to find the minimum of the function.<\/p><p>However, calculating the derivative and equating it to 0 in order to find the corresponding x, does not allow us to find analytical solutions with any certainty.<\/p><p>This is why we use the gradient descent method. To find out more about this technique, see this article.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2eab48ac elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"2eab48ac\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Discover our courses<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/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\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>The notion of derivative is particularly used in DataScience for machine learning models. Apart from what you&#8217;ve probably seen in high school, the applications of this mathematical tool are much broader, and we&#8217;ll come back to them at the end of this article. In this article, you&#8217;ll first learn how to calculate the derivative of [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":172428,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Demystifying Derivatives: Understanding the Core of Calculus<\/title>\n<meta name=\"description\" content=\"Get the math help you need by unraveling the concept of derivatives. This beginner-friendly guide explains what derivatives are and why they matter, making calculus more accessible. 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