{"id":828208,"date":"2024-05-23T17:42:08","date_gmt":"2024-05-23T12:12:08","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=828208"},"modified":"2024-05-23T17:42:08","modified_gmt":"2024-05-23T12:12:08","slug":"basic-concepts-differentiation-formula","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-differentiation-formula\/","title":{"rendered":"Differentiation Formula: 7 Rules, Formula Chart\u00a0"},"content":{"rendered":"\n<p>Differentiation is a basic mathematical concept that deals with the rate at which a function changes. Moreover, it is a mathematical process used to find the derivative of a function. This represents the tangent line\u2019s slope to the function\u2019s graph at any point. Notably, the Differentiation Formula is important for different applications in science, engineering and economics. Read on to learn more in detail about the Differentiation Formulas, Chart, the 7 Rules of Differentiation, Differentiation Formulas for Trigonometric Functions, Differentiation Formulas for Inverse Trigonometric Functions and more.\u00a0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-who-invented-differentiation\">Who Invented Differentiation?<\/h2>\n\n\n\n<p>Differentiation as a part of Calculus was independently developed by Sir Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century. Additionally, Newton\u2019s work concentrated on the motion of objects and the forces acting upon them. On the other hand, Leibniz developed much of the notation used in calculus today. However, their united steps laid the groundwork for everyday calculus.\u00a0<\/p>\n\n\n\n<p class=\"has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\"><strong>Also Read: <\/strong><strong>Difference Between Differentiation and Integration<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-why-is-differentiation-used\">Why is Differentiation Used?<\/h2>\n\n\n\n<p>Moreover, Differentiation is used for many purposes which include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Finding the rate of change:<\/strong> Differentiation allows us to find the rate of change of a function at a specific point. This is useful in many applications, such as optimisation problems and analysing the behaviour of functions.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Solving optimisation problems:<\/strong> Differentiation is used to find the maximum or minimum values of a function. Hence, this is important in optimisation problems in fields like economics, engineering, and business.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Analysing the behaviour of functions:<\/strong> Differentiation also helps understand the behaviour of functions. This includes their increasing or decreasing nature, concavity, and points of inflexion.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-integration-formulas\/\"><strong>Integration Formulas: Examples and Solutions<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-differentiation-formula-chart\">Differentiation Formula Chart<\/h2>\n\n\n\n<p>In addition, here is a chart of common Differentiation Formulas:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>Function\u00a0<\/strong><\/td><td><strong>Derivative\u00a0<\/strong><\/td><\/tr><tr><td>x^n<\/td><td>nx^(n-1)<\/td><\/tr><tr><td>e^x<\/td><td>e^x<\/td><\/tr><tr><td>ln(x)<\/td><td>1\/x<\/td><\/tr><tr><td>sin(x)<\/td><td>cos(x)<\/td><\/tr><tr><td>cos(x)<\/td><td>-sin(x)<\/td><\/tr><tr><td>tan(x)<\/td><td>sec^2(x)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-are-the-7-rules-of-differentiation\">What are the 7 Rules of Differentiation?<\/h2>\n\n\n\n<p>Here are the 7 Rules of Differentiation:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Power Rule<\/li>\n<\/ol>\n\n\n\n<p>The derivative of x^n is nx^(n-1)<\/p>\n\n\n\n<p><strong>The Formula:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/GH2YBEkJIBfrdJVog56tkr6TH2Wx3JG96iT66m-tzq2g0ukKHZdyGKPU9UsmBa4e_-Z7cncJSxDLzZq8e3per5EgOhvDUfyY7V-O2l0mjoU8ADSaqW0a8Q4mEtnx_E8fyCVpvWFOoABSDqIdN_LlMTI\" ><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Sum Rule<\/li>\n<\/ol>\n\n\n\n<p>The derivative of the sum of two functions is the sum of their derivatives.<\/p>\n\n\n\n<p><strong>The Formula:\u00a0<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/xV-Xgw2ZfN56ZV5SoQYXhg3Z6_XdLyuCvKppdroebUJyv9yXvBZSlqiWeDWrLquq6_yD9l7m8eBUoskrH2Psbq15Gh19-zrWr-dTVowb-kQLjM4iSzXPOpzbTcnLD7rDOFYCfSDKi1v1oB1zeSWr6Bo\" ><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>Product Rule<\/li>\n<\/ol>\n\n\n\n<p>The derivative of the product of two functions is given by the product of the first function\u2019s derivative and the second function, plus the product of the first function and the second function\u2019s derivative.<\/p>\n\n\n\n<p><strong>The Formula:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/aTGN94O-k0XDe6nUY9vEYbq8cCDq5a8NbjCyVr19mzP7Wbscl4pWH4xTsD10l0U2u3dKDmuC8rjpXzpeMhN7blDNdqyRP1QI2wjYyvf8-BB1Ou9gJJ-Dva0TsGjbFVv_SlacnPF_GOppyFyM0uh31Dw\" ><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>Quotient Rule<\/li>\n<\/ol>\n\n\n\n<p>The derivative of the quotient of two functions is given by the denominator function times the derivative of the numerator function, minus the numerator function times the derivative of the denominator function, all divided by the square of the denominator function.<\/p>\n\n\n\n<p><strong>The Formula:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/yNyUkOqyUodim6FDJ3HIzv-Gg9FS8oPzorPH46zk5479vwlcOoFVyYPO0z1Izoym8uuRI_ZtBwnbxNt2J1HWpBZnycwC2q_Pznmm-nd3-oahVw2lmdRey2NMIYRh30kfnsDolPzQifU1mTPQd7CoC90\" ><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li>Chain Rule\u00a0<\/li>\n<\/ol>\n\n\n\n<p>The derivative of a composite function is the product of the derivative of the inner function and the derivative of the outer function.<\/p>\n\n\n\n<p><strong>The Formula:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/_IQsI6KspVqSrtTT33N1zTXlslMpyQ7rIdV3Fh37xvjZoLVSDqbn3hhxgU1RhVb0qVTvgk2PITLzF-lj5GVUcmUrjQqV8kI0kVU112POPf46iLJDHoNvnAXUtnpfG3Bwyxa2CN5fC1QTB2wlxhuEYRE\" ><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n<li>Constant Rule<\/li>\n<\/ol>\n\n\n\n<p>The <strong>Formula<\/strong> for the Constant Rule is:\u00a0<\/p>\n\n\n\n<p><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"160\"  height=\"34\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/LHCLfx2fjX4V7427C8qke2rXziql7Cgt0tyGN0zqLhIFot3kA2VxVsy4WhcyZaF15K1v_vV9F3eMPPvvmkObMMma6gmEXxIYLIJS904XOfE74xI7Ch2Co13Cvy5_oLh4KIF8GgFZX5xadZn997SUn80\" > here, <em>k<\/em> is a constant<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"7\">\n<li>Derivative of a Constant<\/li>\n<\/ol>\n\n\n\n<p>The <strong>Formula<\/strong> for the Derivative of a Constant is as follows:<\/p>\n\n\n\n<p><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"74\"  height=\"31\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/J7JFbjCxCwcLGq2x0TVha2elWutN60CirUZ4tqh5NWAnkFFVjA4eCCal023sbCGJIeO_klGL-ak7yJXwEg2MYwameEWZQSyuLzt_OgriB1lZ1F6GRRAhBNOIP9F0vGcesi6gjMWzJbGGphAutIaFK_s\" > here, <em>a<\/em> is a constant<\/p>\n\n\n\n<p class=\"has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concept-types-of-angles\/\"><strong>Different Types of Angles with Formulas and Examples\u00a0<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-differentiation-formulas-for-trigonometric-functions\">Differentiation Formulas for Trigonometric Functions<\/h2>\n\n\n\n<p>Furthermore, here are the 6 basic Trigonometric Functions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Derivative of sin(x):\n<ul class=\"wp-block-list\">\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"140\"  height=\"29\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/j6-scYuoSZQHxTLIbWagwGmiWzmdaji4EoK8h0o7zZBEVOHCPUh2YnfIgKHYI-Ggmgu6J52GL--sUzdE_v6CHO2LIPjvnOkKV_XYzOI7vOHVKL7rmV1eZ3l6a3pXgTKQEoYwUg79Ue5y8tepSaVuTVc\" ><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Derivative of cos(x):\n<ul class=\"wp-block-list\">\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"149\"  height=\"32\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/PQ8GRqNSriqBtAXTmtCtTY3nVFWhr3Vm65WxAiLDdX1Vy4eB69lPUzrKUnL3_xDgoxU6HRT3-kNzhkX1w8r2t_urY9SuqweOtmUK7SxwHQu7diVXMOhXppwLFWaIxzMxHV_SAGWbH2TXiAmxg9xgT2k\" ><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Derivative of tan(x):\n<ul class=\"wp-block-list\">\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"142\"  height=\"31\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/-FLyi6UzdE-EE26ea0KKesrZOyZ2fW5hwB3nlVxPbDy7IJun2QnSNw_A_9Nrn0FY0p57mbIXmxrVc_CzLnXxTS5c--dg3tumM4q8p9uuvhOHT-7v2bsRCa7N7ay778SmpWpi1MTx9Ft8hZ5CnytUh9E\" ><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Derivative of cot(x):\n<ul class=\"wp-block-list\">\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"158\"  height=\"31\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/nOd2YWo__8AM22SCY3A1jP_ui9X4cEzhRDkMrNJfJ8ppeXqY9qT5ggtckWWxGS8nbYCFsaJss_8GMK_YK4eQ9dbKgUdH8wm_Qdk6Q9SHYWKbi79o6_9l0Db1TeqG2h9xr0ecC4hWmEn4YblVonsxCYY\" ><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Derivative of sec(x):\n<ul class=\"wp-block-list\">\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"175\"  height=\"31\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/r2hNI2JqXXBBZOBR5EuM9SDkdir949DGHm9iX8nAxhzwy6oEnFc9J5UJZ5Aun4TK3yFxFbguPUlBJy8briDREIk5Na3H-KjjfWQauvIbVpUyeGspNIIwsP6tZ5UiesXh8q0gJSg6uE5w0JL_xjgFE6M\" ><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Derivative of csc(x):\n<ul class=\"wp-block-list\">\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"189\"  height=\"29\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/yjtTEIOR5onZ3bCOH6CUEZic7IbOAQns5ExqTzSJfFbTxMPrcVLtg0sjYpGyq3eV6THAcKrX5z3HQyOkuHMGwfJHzx8YHxQi9loWS9NATeg47GKCl-Wa2kplMuOY7_a7aEjP4kAn4tRdLhXsQcQYkjU\" ><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-properties-of-determinants\/\"><strong>10 Properties of Determinants: Formulas and Examples\u00a0<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-differentiation-formulas-for-inverse-trigonometric-functions\">Differentiation Formulas for Inverse Trigonometric Functions<\/h2>\n\n\n\n<p>In addition, here are the Differentiation Formulas for Inverse Trigonometric Functions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"166\"  height=\"31\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/tlWXIfje9XXODPYNirsHwgZuvw-lB0RUJqOjvdJ1N-YDM-Our-oI62qZlr5OHiRWrw1dGVNmQ_Lnw02NMRYP46AHurHdbimp9P5-J9UFjH476I37F0TVmf54RlP-ityPvSSanlPAlE6iCgzlYwBooRc\" ><\/li>\n\n\n\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"173\"  height=\"31\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/AXfbipjbhQ0UnSkvqCgf7BIb7INB1627FugFSrW-VDjyNB3TZNBJ201R_Im60S0KXND1iTfsn6Za3RnzGCZtC1wX1VwhxQPZJ3IrXa-yTlsLKmujMSEP0bs73BCiZNRVBMePFktw3GAzEySXC6gFgng\" ><\/li>\n\n\n\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"153\"  height=\"31\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/QrCoXnJGiKDYuK-n69iyjsQaO14tn-YJh4sIC-TKgufkRB5d2h6b_mwChvBh52wEMg9-7we7BDCtuPYuPB_ZjChXx8DX5gNY4yQLATmAjV-zRrGPdtdpmztUkgribcKJD9QxiXrsWmhHvPz0VH0Mfj0\" ><\/li>\n\n\n\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"156\"  height=\"34\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/2Z6pi8iIvQ4BwivpxtmMZ4I-UIk1hEjcpvITb7BYJ9TTLHTqzlK7kAZ3kewCXIgSc_lkXgUAo5lgkMNMFi6z1r_mm53CjjsGtH3XYjGJU5UP3j5LsP7AaQDJh1PQvTT7Qq2xvqNAj-z92BOgYfAxmYw\" ><\/li>\n\n\n\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"175\"  height=\"37\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/xayeA-9JTFfkNNhjn8_xy6eEGiO8ur7I_HXwhnHcdGLjwB-F60m7dtUdisMaGwKy_upfL2hKkprHPXHHzvqJEkUsQTtBD3W8JX1K6oNKSQd6Zsgl6zL8Zolsl4i2VOTKhg38dnzBABcgYGqRHFn9LKQ\" ><\/li>\n\n\n\n<li><img  loading=\"lazy\"  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  width=\"187\"  height=\"36\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/57YwYqdZEt3xjPnxA4RA8gOUP_4ZvgIRBmgP68386UyumhxUaP7RKxIsDPsB-VtfviskJP-NIcYyD9HACMgoDStHPnj3dhFOoo8j68k5jOEeHzY7aCfKyUuk4hZptGVmTOeyHkWzv2xQYTVNu9L-Odo\" ><\/li>\n<\/ul>\n\n\n\n<p class=\"has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/average-cost-questions-formulas-and-solved-examples\/\"><strong>Average Cost Questions: Formulas and Solved Examples<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-differentiation-formula-for-division\">Differentiation Formula for Division<\/h2>\n\n\n\n<p>The Differentiation Formula for division is:<\/p>\n\n\n\n<p>d \/ dx [ f (x) \/ g (x)] = [ g (x) f\u2019 (x) \u2013 f (x) g\u2019 (x) ] \/ [ g (x) ]^2<\/p>\n\n\n\n<p>where f'(x) and g'(x) are the derivatives of f(x) and g(x), respectively.<\/p>\n\n\n\n<p><strong>For Example:<\/strong>\u00a0<\/p>\n\n\n\n<p>Say that you have the function y = (x^2 + 1) \/ (x \u2013 2). You want to find the derivative dy\/dx.<\/p>\n\n\n\n<p>Using the Differentiation formula for division:<\/p>\n\n\n\n<p>d \/ dx [ f (x) \/ g (x)] = [ g (x) f\u2019 (x) \u2013 f (x) g\u2019 (x) ] \/ [ g (x) ]^2<\/p>\n\n\n\n<p>Where,<\/p>\n\n\n\n<p>f(x) = x^2 + 1<\/p>\n\n\n\n<p>g(x) = x \u2013 2<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Find the derivatives of f(x) and g(x).<\/p>\n\n\n\n<p>f'(x) = d \/ dx (x^2 + 1) = 2x<\/p>\n\n\n\n<p>g'(x) = d \/ dx (x \u2013 2) = 1<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Substitute the functions and their derivatives into the formula.<\/p>\n\n\n\n<p>dy \/ dx = [ (x \u2013 2) (2x) \u2013 (x^2 + 1) (1) ] \/ [ (x \u2013 2)^2]<\/p>\n\n\n\n<p>= [2x^2 \u2013 2x \u2013 2x^2 \u2013 1] \/ [(x \u2013 2)^2]<\/p>\n\n\n\n<p>= [-2x^2 \u2013 2x \u2013 1] \/ [(x \u2013 2)^2]<\/p>\n\n\n\n<p><strong>Step 3:<\/strong> Simplify the expression.<\/p>\n\n\n\n<p>dy\/dx = -2x^2 \u2013 2x \u2013 1 \/ (x \u2013 2)^2<\/p>\n\n\n\n<p>Therefore, the Derivative of y = (x^2 + 1) \/ (x \u2013 2) is dy \/ dx = -2x^2 \u2013 2x \u2013 1 \/ (x \u2013 2)^2.<\/p>\n\n\n\n<p class=\"has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\"><strong>Also Read: <\/strong><strong>What is the Difference Between Dot Product and Cross Product?<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-do-you-calculate-dy-dx\">How do you Calculate dy dx?<\/h2>\n\n\n\n<p>To calculate dy\/dx, you need to use the Differentiation formulas and rules. Here is the usual approach:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Identify the function y = f(x).<\/li>\n\n\n\n<li>Apply the appropriate Differentiation formula or rule based on the function\u2019s structure.<\/li>\n\n\n\n<li>Simplify the resulting expression to obtain dy\/dx.<\/li>\n<\/ol>\n\n\n\n<p><strong>For Example:<\/strong><\/p>\n\n\n\n<p>To calculate dy\/dx, you need to consider an example where you have the function y = 3x^2 + 2x \u2013 5.\u00a0<\/p>\n\n\n\n<p>To find dy\/dx for this function, you need to Differentiate it with x using the power rule and the sum rule of differentiation.<\/p>\n\n\n\n<p>Given function: y = 3x^2 + 2x \u2013 5<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find dy\/dx for each term: For the term 3x^2: d\/dx (3x^2) = 3 * 2x = 6x<\/li>\n<\/ol>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Combine the derivatives of each term using the sum rule:<br>dy \/ dx = d \/ dx (3x^2) + d \/ dx (2x) + d \/ dx (-5)<br>= 6x + 2 + 0<br>= 6x + 2<\/li>\n<\/ol>\n\n\n\n<p>Therefore, the derivative of y = 3x^2 + 2x \u2013 5 with x is dy \/ dx = 6x + 2. Thus, this result represents the rate of change of the function y with x at any given point.<\/p>\n\n\n\n<p class=\"has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-surface-area-of-a-cuboid\/\"><strong>Surface Area of a Cuboid: Definition, Derivation and Formula<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-differentiation-of-2x\">What is the Differentiation of 2x?<\/h2>\n\n\n\n<p>The differentiation of 2x is:<\/p>\n\n\n\n<p>d \/ dx (2x) = 2 \u2715 d \/ dx (x) = 2 \u2715 1 = 2<\/p>\n\n\n\n<p>where you use the Constant rule and the Power rule.<\/p>\n\n\n\n<p class=\"has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concept-trigonometry-formulas\/\"><strong>Trigonometry Formulas, Examples and Solutions!<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-to-differentiate-a-sum\">How to Differentiate a Sum?<\/h2>\n\n\n\n<p>To differentiate a Sum, you use the Sum rule. The derivative of a Sum of functions is the Sum of their derivatives.\u00a0<\/p>\n\n\n\n<p><strong>For example<\/strong>, if y = f(x) + g(x), then:<\/p>\n\n\n\n<p>dy \/ dx = d \/ dx [ f (x) + g (x) ] = d \/ dx [ f (x) ] + d \/d x [ g(x) ]<\/p>\n\n\n\n<p>Thus, you Differentiate each term separately and then add the results together.<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-b9eb360a4bc4bdaa3c4feb84a1bd0d67\"><strong>Related Blogs\u00a0<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-types-of-fractions\/\"><strong>7 Types of Fractions with Examples<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-hcf-and-lcm\/\"><strong>All You Need to Know About HCF and LCM\u00a0<\/strong><\/a><\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-how-to-find-percentage-of-marks\/\"><strong>How to Find Percentage of Marks?<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-tables-1-to-20\/\"><strong>Multiplication Tables of 1 to 20<\/strong><\/a><\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concept-hcf-of-two-consecutive-numbers\/\"><strong>What is the HCF of Two Consecutive Numbers?<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/civics-and-polity-table-of-17\/\"><strong>Table of 17: Multiples up to 20 & a Trick!<\/strong><\/a>\u00a0\u00a0<\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-table-of-12\/\"><strong>Table of 12: Multiples up to 20!<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concept-hcf-of-two-consecutive-odd-numbers\/\"><strong>What is the HCF of Two Consecutive Odd Numbers?<\/strong><\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>I hope this helps! Did you like learning about the Differentiation Formula? Keep reading our blogs to learn more about the <a href=\"https:\/\/leverageedu.com\/discover\/category\/school-education\/basic-concepts\/maths\/\"><strong>Basic Concepts of Maths<\/strong><\/a>!<\/p>\n","protected":false},"excerpt":{"rendered":"Differentiation is a basic mathematical concept that deals with the rate at which a function changes. Moreover, it&hellip;\n","protected":false},"author":106,"featured_media":828215,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[423,476,389],"tags":[],"class_list":{"0":"post-828208","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-basic-concepts","8":"category-maths","9":"category-school-education"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.5 (Yoast SEO v27.5) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Differentiation Formula: 7 Rules, Formula Chart\u00a0 - Leverage Edu Discover<\/title>\n<meta name=\"description\" content=\"Differentiation formula is a basic mathematical concept that deals with the rate at which a function changes.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-differentiation-formula\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Differentiation Formula: 7 Rules, Formula Chart\u00a0\" \/>\n<meta property=\"og:description\" content=\"Differentiation formula is a basic mathematical concept that deals with the rate at which a function changes.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-differentiation-formula\/\" \/>\n<meta property=\"og:site_name\" content=\"Leverage Edu Discover\" \/>\n<meta property=\"article:published_time\" content=\"2024-05-23T12:12:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogassets.leverageedu.com\/media\/uploads\/sites\/9\/2024\/05\/14120709\/Differentiation-Formula.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"640\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Santana Daphne Antunis\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Santana Daphne Antunis\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Differentiation Formula: 7 Rules, Formula Chart\u00a0 - 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Talk to me about any topic under the sun, especially sustainability, art, music and photography.","url":"https:\/\/leverageedu.com\/discover\/author\/santana\/"}]}},"acf":[],"_links":{"self":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/828208","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/users\/106"}],"replies":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/comments?post=828208"}],"version-history":[{"count":0,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/828208\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media\/828215"}],"wp:attachment":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media?parent=828208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/categories?post=828208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/tags?post=828208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}