https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:derivatives/v/calculus-derivatives-1-new-hd-version 2025-01-06T10:18:43.365910625Z एक सीमा के रूप में अवकलज की औपचारिक परिभाषा (Formal definition of the derivative as a limit) Discover how to define the derivative of a function at a specific point using the limit of the slope of the secant line. We'll explore the concept of finding the slope as the difference in function values approaches zero, represented by the limit of [f(c)-f(c+h)]/h as h→0. Sal Khan video https://cdn.kastatic.org/googleusercontent/f7edMdKGwytIJfVv9f8HZGykIr5fXzJ9eLpF7VFA2Y7DPQw7Zlq6wbdK1Rf2gsf5e8f8usxTd5xd5wz2nxJplqM एक सीमा के रूप में अवकलज की औपचारिक परिभाषा (Formal definition of the derivative as a limit) Discover how to define the derivative of a function at a specific point using the limit of the slope of the secant line. We'll explore the concept of finding the slope as the difference in function values approaches zero, represented by the limit of [f(c)-f(c+h)]/h as h→0. https://cdn.kastatic.org/ka-youtube-converted/oW99efgEkU4.mp4/oW99efgEkU4.mp4 943 अवकलजों की भूमिका (Derivatives Introduction) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:derivatives/v/alternate-form-of-the-derivative 2025-01-07T14:22:35.748578099Z अवकलज का औपचारिक तथा वैकल्पिक रूप (Formal and alternate form of the derivative) Discover the two methods for defining the derivative of a function at a specific point using limit expressions. In this video we'll explore the standard form and alternate form, enhancing our understanding of tangent line slopes and secant line approximations. Sal Khan video https://cdn.kastatic.org/googleusercontent/RJ5ynAu__DEqYV6GmzDEfo0ZPvcyf5YkTi2W4gXktvh7WpA_ruD8LKnpPY1Ij_wxkB-2ym0HezKSnhR6QSshcbPX अवकलज का औपचारिक तथा वैकल्पिक रूप (Formal and alternate form of the derivative) Discover the two methods for defining the derivative of a function at a specific point using limit expressions. In this video we'll explore the standard form and alternate form, enhancing our understanding of tangent line slopes and secant line approximations. https://cdn.kastatic.org/ka-youtube-converted/EXxd39zPLms.mp4/EXxd39zPLms.mp4 293 अवकलजों की भूमिका (Derivatives Introduction) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:derivatives/v/formal-and-alternate-form-of-the-derivative-for-ln-x 2025-01-07T14:22:35.748578099Z उदाहरण : एक सीमा के रूप में अवकलज (Worked example: Derivative as a limit) Discover how to apply the formal and alternate forms of the derivative in real-world scenarios. We'll explore the process of finding the slope of tangent lines using both methods and compare their effectiveness in solving calculus problems. Let's dive into the practical side of derivatives to deepen our understanding. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw उदाहरण : एक सीमा के रूप में अवकलज (Worked example: Derivative as a limit) Discover how to apply the formal and alternate forms of the derivative in real-world scenarios. We'll explore the process of finding the slope of tangent lines using both methods and compare their effectiveness in solving calculus problems. Let's dive into the practical side of derivatives to deepen our understanding. https://cdn.kastatic.org/ka-youtube-converted/oyG3czt3LHc.mp4/oyG3czt3LHc.mp4 346 अवकलजों की भूमिका (Derivatives Introduction) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivatives-introduction/v/formal-and-alternate-form-of-the-derivative-example-1 2025-01-07T14:22:35.748578099Z उदाहरण : सीमा व्यंजक से अवकलज (Worked example: Derivative from limit expression) We explore a limit expression and discover that it represents the derivative of the function f(x) = x³ at the point x = 5. By analyzing the alternate form of the derivative, we gain a deeper understanding of tangent lines and their slopes. Sal Khan video https://cdn.kastatic.org/googleusercontent/mRb04hmxds73ZL_sMNXBuSvgJWIEdDWaFqII1RDcrdsyueWxuoNan8KXuqI5CEwLvxcoRGQOL2CXmaQbgNqDVYE उदाहरण : सीमा व्यंजक से अवकलज (Worked example: Derivative from limit expression) We explore a limit expression and discover that it represents the derivative of the function f(x) = x³ at the point x = 5. By analyzing the alternate form of the derivative, we gain a deeper understanding of tangent lines and their slopes. https://cdn.kastatic.org/ka-youtube-converted/jwxffRYXGrU.mp4/jwxffRYXGrU.mp4 317 अवकलजों की भूमिका (Derivatives Introduction) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivatives-introduction/v/derivatives-using-first-principle 2025-06-25T04:36:24.163902917Z प्रथम सिद्धांत के उपयोग से अवकलज In this video, we'll solve two problems where we find the limit of functins from first principle. Through these problems, we'll learn the strategies that we can use to find limits in such problems. We first find the derivative of 1/x^2 and then of tan(x). In both of these, step 1 is to use the first principle and plug in the value for f(x). Step 2 is manipulation - algebraic or trigonometric. Step 3 is getting rid of h - either through direct plugging or by using some simpler functions limit. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw प्रथम सिद्धांत के उपयोग से अवकलज In this video, we'll solve two problems where we find the limit of functins from first principle. Through these problems, we'll learn the strategies that we can use to find limits in such problems. We first find the derivative of 1/x^2 and then of tan(x). In both of these, step 1 is to use the first principle and plug in the value for f(x). Step 2 is manipulation - algebraic or trigonometric. Step 3 is getting rid of h - either through direct plugging or by using some simpler functions limit. https://cdn.kastatic.org/ka-youtube-converted/E16ONTO3nI8.mp4/E16ONTO3nI8.mp4 329 अवकलजों की भूमिका (Derivatives Introduction) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:derivatives/e/the-formal-and-alternate-form-of-the-derivative 2025-04-09T10:40:17.096567662Z सीमा के रूप में अवकलज(Derivative as a limit) फलनों के अवकलजों (derivatives) को सीमा व्यंजकों के रूप में लिखें। Tomer Gal exercise https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:derivatives/v/power-rule 2025-01-07T14:22:35.748578099Z घात नियम (Power rule) Let's dive into the power rule, a handy tool for finding the derivative of xⁿ. This rule simplifies the process of taking derivatives, especially for polynomials, by bringing the exponent out front and decrementing the power. We explore examples with positive, negative, and fractional exponents. Sal Khan video https://cdn.kastatic.org/googleusercontent/ep8pwcOTRuIUd4vjC92ZocRoYYB4y_bepmbnrR4FiJ25ltdCz6L4Az5ca1qhdj7L7rKY0yAazbXDABwd40BLLL48 घात नियम (Power rule) Let's dive into the power rule, a handy tool for finding the derivative of xⁿ. This rule simplifies the process of taking derivatives, especially for polynomials, by bringing the exponent out front and decrementing the power. We explore examples with positive, negative, and fractional exponents. https://cdn.kastatic.org/ka-youtube-converted/aSiWbZMRLbM.mp4/aSiWbZMRLbM.mp4 234 अवकलजों की भूमिका (Derivatives Introduction) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivatives-introduction/e/power-rule-intro 2025-04-09T10:40:17.096567662Z घात नियम (धनात्मक पूर्णांक घात){Power rule (positive integer powers)} xⁿ के रूप के फलनों को विभेदित करने के लिए घात नियम का उपयोग करें, जहाँ n एक धनात्मक पूर्णांक है। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivatives-introduction/e/differentiate-negative-powers 2025-04-09T10:40:17.096567662Z घात नियम (ऋणात्मक और भिन्नात्मक घात){Power rule (negative & fractional powers)} xⁿ के रूप के फलनों को विभेदित करने के लिए घात नियम का उपयोग करें, जहाँ n एक ऋणात्मक पूर्णांक या भिन्न है। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivatives-introduction/v/power-rule-with-rewriting 2025-01-07T14:22:35.748578099Z घात नियम (व्यंजक को पुनः लिखने के साथ) [Power rule (with rewriting the expression)] Discover how the power rule helps us find derivatives of functions like 1/x, ∛x, or ∛x². By rewriting these functions as xⁿ, where n is a negative or fractional exponent, we can apply the power rule to calculate their derivatives with ease. video https://cdn.kastatic.org/googleusercontent/iloQtEvwi681cOiNQDTDAFZp0HEWF_UYwBJ5WnqTPL_QPzXbhoL8ubebuSSiWljErut5ASmmcQb9L0MdMu-_TCI घात नियम (व्यंजक को पुनः लिखने के साथ) [Power rule (with rewriting the expression)] Discover how the power rule helps us find derivatives of functions like 1/x, ∛x, or ∛x². By rewriting these functions as xⁿ, where n is a negative or fractional exponent, we can apply the power rule to calculate their derivatives with ease. https://cdn.kastatic.org/ka-youtube-converted/5KJzxF2Ngyk.mp4/5KJzxF2Ngyk.mp4 264 अवकलजों की भूमिका (Derivatives Introduction) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:derivatives/e/differentiate-fractional-powers 2025-04-09T10:40:17.096567662Z घात नियम (व्यंजक को पुनः लिखने के साथ) [Power rule (with rewriting the expression)] ∜x³ और 1/x² जैसे व्यंजकों के अवकलजों को xⁿ के रूप में पुनः लिखकर तथा घात नियम का उपयोग करके ज्ञात करें और उनका मूल्यांकन करें। Tomer Gal exercise