{"id":5121,"date":"2021-09-08T18:15:52","date_gmt":"2021-09-08T12:45:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=5121"},"modified":"2022-09-16T02:06:40","modified_gmt":"2022-09-15T20:36:40","slug":"differentiation-formulas-class-12","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/differentiation-formulas-class-12\/","title":{"rendered":"Differentiation Formulas Class 12 – Calculus"},"content":{"rendered":"

Here you will learn what is derivative or differentiation and various differentiation formulas class 12.<\/p>\n

Let’s begin –<\/p>\n

What is Derivative or Differentiation ?<\/h2>\n

Let f(x) be a differentiable or derivable function on [a, b]. Then,<\/p>\n

\\(lim_{h \\to 0}\\) \\(f(x + h) – f(x)\\over h\\)\u00a0 \u00a0or,\u00a0 \\(lim_{h \\to 0}\\) \\(f(x – h) – f(x)\\over -h\\)<\/p>\n

is called the derivative or differentiation<\/strong> of f(x) with respect to x and is denoted by<\/p>\n

f'(x) or, \\(d\\over dx\\) (f(x))\u00a0 or,\u00a0 Df(x),\u00a0 where D = \\(d\\over dx\\)<\/p>\n

Sometimes the derivative or differentiation of the function f(x) is called the differential coefficient of f(x). The process of finding the derivative of a function by using the above definition is called the differentiation from first principles or by ab-initio method or by delta method.<\/p>\n

Differentiation Formulas Class 12<\/h2>\n

Following are derivatives or differentiation of some standard functions.<\/p>\n

Basic Differentiation Formulas<\/h3>\n

(i)<\/strong>\u00a0 \\(d\\over dx\\) \\(x^n\\) = \\(nx^{n-1}\\)<\/p>\n

(ii)<\/strong>\u00a0 \\(d\\over dx\\)(a) = 0,\u00a0 \u00a0 \u00a0where a is constant.<\/p>\n

(iii)<\/strong>\u00a0 \u00a0\\(d\\over dx\\)(x) = 1<\/p>\n

(iv)<\/strong>\u00a0 \\(d\\over dx\\)(kx) = k,\u00a0 \u00a0 where k is constant<\/p>\n

Differentiation of Logarithmic and Exponential Function Formulas<\/h3>\n

(i)<\/strong>\u00a0 \u00a0\\(d\\over dx\\) \\(e^x\\) = \\(e^x\\)<\/p>\n

(ii)<\/strong>\u00a0 \\(d\\over dx\\) \\(a^x\\) = \\(a^xlog_e a\\)<\/p>\n

(iii)<\/strong>\u00a0 \\(d\\over dx\\) \\(log_e x\\) = \\(1\\over x\\)<\/p>\n

(iv)<\/strong>\u00a0 \\(d\\over dx\\) \\(log_a x\\) = \\(1\\over xlog_e a\\)<\/p>\n

Trigonometric Function Differentiation Formulas Class 12<\/h3>\n

(i)<\/strong>\u00a0 \\(d\\over dx\\) (sin x) = cos x<\/p>\n

(ii)<\/strong>\u00a0 \\(d\\over dx\\) (cos x) = – sin x<\/p>\n

(iii)<\/strong>\u00a0 \\(d\\over dx\\) (tan x) = \\(sec^2 x\\)<\/p>\n

(iv)<\/strong>\u00a0 \\(d\\over dx\\) (cot x) = \\(- cosec^2 x\\)<\/p>\n

(vi)<\/strong>\u00a0 \\(d\\over dx\\) (sec x) = sec x tan x<\/p>\n

(vi)<\/strong>\u00a0 \\(d\\over dx\\) (cosec x) = – cosec x cot x<\/p>\n

Inverse Trigonometric Function Differentiation Formulas<\/h3>\n

(i)<\/strong>\u00a0 \\(d\\over dx\\) \\(sin^{-1} x\\) = \\(1\\over {\\sqrt{1 – x^2}}\\)<\/p>\n

(ii)<\/strong>\u00a0 \\(d\\over dx\\) \\(cos^{-1} x\\) = – \\(1\\over {\\sqrt{1 – x^2}}\\)<\/p>\n

(iii)<\/strong>\u00a0 \\(d\\over dx\\) \\(tan^{-1} x\\) = \\(1\\over {1 + x^2}\\)<\/p>\n

(iv)<\/strong>\u00a0 \\(d\\over dx\\) \\(cot^{-1} x\\) = -\\(1\\over {1 + x^2}\\)<\/p>\n

(v)<\/strong>\u00a0 \\(d\\over dx\\) \\(sec^{-1} x\\) = \\(1\\over {| x |\\sqrt{x^2 – 1}}\\)<\/p>\n

(vi)<\/strong>\u00a0 \\(d\\over dx\\) \\(cosec^{-1} x\\) =\u00a0 – \\(1\\over {| x |\\sqrt{x^2 – 1}}\\)<\/p>\n

Differentiation Rules Class 12<\/h3>\n

(i)\u00a0 Product Rule<\/a><\/strong> – \\(d\\over dx\\) {f(x) g(x)} = \\(d\\over dx\\) (f(x)) g(x) + f(x). \\(d\\over dx\\) (g(x))<\/p>\n

(ii)\u00a0 Quotient Rule<\/a><\/strong> – \\({g(x) {d\\over dx} (f(x)) – f(x) {d\\over dx} (g(x))}\\over {(g(x))^2}\\)<\/p>\n

(iii)\u00a0 Chain Rule<\/a><\/strong> – \\(d\\over dx\\) {(fog) (x)} = \\(d\\over d g(x)\\) {(fog) (x)} \\(d\\over dx\\) (g(x)).<\/p>\n\n\n

\n
Next – Product Rule in Differentiation with Examples<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is derivative or differentiation and various differentiation formulas class 12. Let’s begin – What is Derivative or Differentiation ? Let f(x) be a differentiable or derivable function on [a, b]. Then, \\(lim_{h \\to 0}\\) \\(f(x + h) – f(x)\\over h\\)\u00a0 \u00a0or,\u00a0 \\(lim_{h \\to 0}\\) \\(f(x – h) – f(x)\\over -h\\) …<\/p>\n

Differentiation Formulas Class 12 – Calculus<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[36],"tags":[275,331,332],"yoast_head":"\nDifferentiation Formulas Class 12 - Calculus - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn what is derivative or differentiation and various differentiation formulas class 12.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/differentiation-formulas-class-12\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Differentiation Formulas Class 12 - 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