https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/v/differentiability-at-a-point-algebraic-not-differentiable 2024-10-23T16:58:31.217736248Z किसी बिंदु पर अवकलनीयता: बीज गणितीय फलन जो अवकलनीय नहीं We examine a piecewise function to determine its differentiability and continuity at an edge point. Through analyzing left and right-hand limits, we find that the function is continuous at the point. However, due to differing slopes from the left and right, the function is not differentiable at the edge point. video https://cdn.kastatic.org/ka_thumbnails_cache/28a81671-858e-4bf2-adf6-3dc89b196a7e_1280_720_base.png किसी बिंदु पर अवकलनीयता: बीज गणितीय फलन जो अवकलनीय नहीं We examine a piecewise function to determine its differentiability and continuity at an edge point. Through analyzing left and right-hand limits, we find that the function is continuous at the point. However, due to differing slopes from the left and right, the function is not differentiable at the edge point. https://cdn.kastatic.org/ka-youtube-converted/k0BB2YFWoyc.mp4/k0BB2YFWoyc.mp4 382 अवकलनीयता https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:continuity-and-differentiability/e/differentiability-at-a-point-algebraic 2025-09-05T11:35:10.064338248Z बिन्दु पर अवकलनीयता (Differentiability): बीजगणितीय बीजगणितीय फलन का विश्लेषण करें जिससे यह ज्ञात हो सके कि वे दिए गए बिन्दु पर संतत और/या अवकलनीय हैं या नहीं। Tomer Gal exercise https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/v/derivative-properties-and-polynomial-derivatives 2024-10-23T16:58:31.217736248Z आधारभूत अवकलज नियम (Basic derivative rules) Let's explore how to find the derivative of any polynomial using the power rule and additional properties. The derivative of a constant is always 0, and we can pull out a scalar constant when taking the derivative. Furthermore, the derivative of a sum of two functions is simply the sum of their derivatives. Sal Khan video https://cdn.kastatic.org/googleusercontent/518kcwioa0AcVYYwRMuZ53FfjtCKnXqyp7_jKbrCaJimmfPcewLLBSTVJyOM5tJnAEqj1CFkQpPjMUHJjkhb3Jc आधारभूत अवकलज नियम (Basic derivative rules) Let's explore how to find the derivative of any polynomial using the power rule and additional properties. The derivative of a constant is always 0, and we can pull out a scalar constant when taking the derivative. Furthermore, the derivative of a sum of two functions is simply the sum of their derivatives. https://cdn.kastatic.org/ka-youtube-converted/xx6LdfCKXuE.mp4/xx6LdfCKXuE.mp4 593 अवकलनीयता https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:continuity-and-differentiability/e/differentiate-composite-functions-intro 2024-10-23T11:40:14.281463186Z शृंखला नियम (chain rule) परिचय शृंखला नियम का उपयोग करके संयुक्त फलन जैसे sin(2x+1) या [cos(x)]³ का अवकलन (differentiation) करें: Tomer Gal exercise https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/e/differentiate-composite-functions 2025-03-27T04:12:32.118655087Z संयुक्त फलनों (composite functions) का अवकलन करें (सभी प्रकार के फलन) शृंखला नियम (chain rule) का उपयोग करके दो (अधिक बुनियादी) फलनों के संयोजन से बने फलनों का अवकलज निकालें। Tomer Gal exercise https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/v/applying-the-chain-rule-and-product-rule 2024-10-23T16:58:31.217736248Z श्रृंखला नियम और गुणन नियम का प्रयोग करना Let's explore multiple strategies to tackle derivatives involving both the product and chain rules. We start by applying the chain rule first, then the product rule. Next, we switch it up, using the product rule first, then the chain rule. Discover how these different approaches lead us to the same answer, demonstrating the flexibility and interconnectedness of these mathematical rules. video https://cdn.kastatic.org/ka_thumbnails_cache/5944fb24-452d-4084-9dd1-d1bbdabebb96_1280_720_base.png श्रृंखला नियम और गुणन नियम का प्रयोग करना Let's explore multiple strategies to tackle derivatives involving both the product and chain rules. We start by applying the chain rule first, then the product rule. Next, we switch it up, using the product rule first, then the chain rule. Discover how these different approaches lead us to the same answer, demonstrating the flexibility and interconnectedness of these mathematical rules. https://cdn.kastatic.org/ka-youtube-converted/a_h2ouF41Zs.mp4/a_h2ouF41Zs.mp4 354 अवकलनीयता https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/e/exp-log-trig-radical-composite-diff 2025-06-25T04:37:22.958747522Z शृंखला नियम विविधीय (Chain rule capstone) चरघातांकी (exponential), लघुगणकीय (logarithmic), त्रिकोणमितीय (trigonometric) और मूल (radical) फलन जिनके आंतरिक फलन बहुपदीय (polynomial) हैं, उनके अवकलज (derivatives) निकालें। Tomer Gal exercise https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:continuity-and-differentiability/v/implicit-differentiation-1 2024-10-23T16:58:31.217736248Z अस्पष्ट अवकलन Some relationships cannot be represented by an explicit function. For example, x²+y²=1. Implicit differentiation helps us find ​dy/dx even for relationships like that. This is done using the chain ​rule, and viewing y as an implicit function of x. For example, according to the chain rule, the derivative of y² would be 2y⋅(dy/dx). Sal Khan video https://cdn.kastatic.org/googleusercontent/J3IuW_SdB3YQgggI2OZHsoN8vmEIRuzq-U6_vX3OPTsL_FymniZfpKb5rUJhtAjMv_E0A_kP_FUEUZ8QVQmS1hHJ अस्पष्ट अवकलन Some relationships cannot be represented by an explicit function. For example, x²+y²=1. Implicit differentiation helps us find ​dy/dx even for relationships like that. This is done using the chain ​rule, and viewing y as an implicit function of x. For example, according to the chain rule, the derivative of y² would be 2y⋅(dy/dx). https://cdn.kastatic.org/ka-youtube-converted/xRs7UF-grrs.mp4/xRs7UF-grrs.mp4 482 अवकलनीयता https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:continuity-and-differentiability/e/implicit-differentiation 2025-06-25T04:37:22.958747522Z अस्पष्ट अवकलन अस्पष्ट अवकलन (implicit differentiation) का प्रयोग कर अभ्यास करें। Tomer Gal exercise https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/v/derivative-inverse-sine 2025-01-15T06:58:22.059959256Z sine के प्रतिलोम का अवकलज (Derivative of inverse sine) Unlock the mystery of the derivative of inverse sine! Let's dive into the world of calculus, rearranging equations and applying implicit differentiation to find the derivative of y with respect to x. Using trigonometric identities, we transform the derivative into a function of x, revealing a fascinating relationship. Sal Khan video https://cdn.kastatic.org/googleusercontent/TC-D-ES3wUzt8Qplru972T5gPY59R5SLsMvo-hWbmKjf9Rnhlt9RcNuPt23kV_0NB5hrYnpqTXsd-O4wP32xctFOig sine के प्रतिलोम का अवकलज (Derivative of inverse sine) Unlock the mystery of the derivative of inverse sine! Let's dive into the world of calculus, rearranging equations and applying implicit differentiation to find the derivative of y with respect to x. Using trigonometric identities, we transform the derivative into a function of x, revealing a fascinating relationship. https://cdn.kastatic.org/ka-youtube-converted/C0SYdjJ-mjs.mp4/C0SYdjJ-mjs.mp4 296 अवकलनीयता https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/v/derivative-inverse-cosine 2025-08-25T11:24:50.796694667Z cosine के प्रतिलोम का अवकलज (Derivative of inverse cosine) Unraveling the mystery of the inverse cosine function, we find its derivative equals -1/(sqrt(1 - x^2)). This step-by-step proof guides us to a fascinating comparison with the derivative of inverse sine, revealing a captivating connection between these two trigonometric functions. Sal Khan video https://cdn.kastatic.org/googleusercontent/xD9q4NJ8qH9IMBxQhEvVVZrvt43R-vuoPevtrTigfTAGX82bI1XBDAEmCzu26a_B63_ZCRAqSQn2sAEvXWhwi58 cosine के प्रतिलोम का अवकलज (Derivative of inverse cosine) Unraveling the mystery of the inverse cosine function, we find its derivative equals -1/(sqrt(1 - x^2)). This step-by-step proof guides us to a fascinating comparison with the derivative of inverse sine, revealing a captivating connection between these two trigonometric functions. https://cdn.kastatic.org/ka-youtube-converted/VKuZzulvDvI.mp4/VKuZzulvDvI.mp4 224 अवकलनीयता https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/v/derivative-inverse-tangent 2025-08-25T11:24:50.796694667Z tangent के प्रतिलोम का अवकलज (Derivative of inverse tangent) Now let's explore the derivative of the inverse tangent function. Starting with the derivative of tangent, we use the chain rule and trigonometric identities to find the derivative of its inverse. Join us as we investigate this fascinating mathematical process! Sal Khan video https://cdn.kastatic.org/googleusercontent/f0bVGN6g1oYXxST0OHEmXjlgAhdT_fYwKolK1lXe4QrIJ4-QMJ4cCGtHmTvRYRdbJQ87mFs0vYt77vKcsK9a0F6OeQ tangent के प्रतिलोम का अवकलज (Derivative of inverse tangent) Now let's explore the derivative of the inverse tangent function. Starting with the derivative of tangent, we use the chain rule and trigonometric identities to find the derivative of its inverse. Join us as we investigate this fascinating mathematical process! https://cdn.kastatic.org/ka-youtube-converted/oYUXd1ErVA8.mp4/oYUXd1ErVA8.mp4 362 अवकलनीयता https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-887/e/derivatives-of-inverse-trigonometric-functions 2025-06-25T04:37:22.958747522Z प्रतिलोम त्रिकोणमितीय फलन के अवकलज (Derivatives) ऐसे फलनों का अवकलन करें जिनमें प्रतिलोम त्रिकोणमितीय फलन arcsin(x), arccos(x) और arctan(x) शामिल हों। Tomer Gal exercise