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 फलनों के अवकलजों का बीजगणित (Algebra of derivatives of functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:algebra-of-derivatives-of-functions/v/differentiating-linear-functions 2025-01-06T10:18:43.365910625Z आधारभूत अवकलज नियम :त्रुटि पकड़ना (Basic derivative rules: Find the error) We analyze two students' attempts to differentiate linear functions using basic rules. One student forgets a negative sign, while another incorrectly assumes the derivative of a product equals the product of derivatives. By identifying common mistakes, we help improve our understanding of differentiation. video https://cdn.kastatic.org/ka_thumbnails_cache/28ec41a5-9984-4553-8e7b-9a9d41f2ec7c_1280_720_base.png आधारभूत अवकलज नियम :त्रुटि पकड़ना (Basic derivative rules: Find the error) We analyze two students' attempts to differentiate linear functions using basic rules. One student forgets a negative sign, while another incorrectly assumes the derivative of a product equals the product of derivatives. By identifying common mistakes, we help improve our understanding of differentiation. https://cdn.kastatic.org/ka-youtube-converted/h3saCvnS2W0.mp4/h3saCvnS2W0.mp4 286 फलनों के अवकलजों का बीजगणित (Algebra of derivatives of functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:algebra-of-derivatives-of-functions/e/differentiating-linear-functions 2025-04-09T10:40:17.096567662Z आधारभूत अवकलज नियम :त्रुटि पकड़ना (Basic derivative rules: Find the error) आधारभूत विभेदन नियमों का उपयोग करके रैखिक फलनों के अवकलज ज्ञात करने के लिए समाधानों (solutions) का विश्लेषण करें। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:algebra-of-derivatives-of-functions/e/basic-differentiation-rules 2025-04-09T10:40:17.096567662Z आधारभूत अवकलज नियम : तालिका(Basic derivative rules:table) संयुक्त फलनों के अवकलजों का मूल्यांकन करने के लिए आधारभूत विभेदन नियमों का उपयोग करें। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:algebra-of-derivatives-of-functions/v/applying-the-product-rule-for-derivatives 2025-01-06T10:18:03.589731621Z गुणन नियम (Product rule) Discover the product rule, a fundamental technique for finding the derivative of a function expressed as a product of two functions. We'll learn how to apply this rule to simplify differentiation and enhance our understanding of calculus. Sal Khan video https://cdn.kastatic.org/googleusercontent/gvxut2GAowO-jcx3gFpqOrHgtqwIaXYASRloUizkAbyX3oyOqCb455SbDI8VD4HmrHtgv0_qW1PsPqg3Pb0es1xV गुणन नियम (Product rule) Discover the product rule, a fundamental technique for finding the derivative of a function expressed as a product of two functions. We'll learn how to apply this rule to simplify differentiation and enhance our understanding of calculus. https://cdn.kastatic.org/ka-youtube-converted/4863ig3oEb4.mp4/4863ig3oEb4.mp4 160 फलनों के अवकलजों का बीजगणित (Algebra of derivatives of functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:algebra-of-derivatives-of-functions/v/differentiating-products 2025-01-06T10:18:03.589731621Z गुणन का अवकलन (Differentiating products) We explore the product rule by finding the derivative of eˣcos(x). We identify eˣ as the first function and cos(x) as the second, then apply the product rule to calculate the derivative, simplifying our result for a clearer understanding. video https://cdn.kastatic.org/ka_thumbnails_cache/44c67ae6-dddf-4707-a4dd-af68bf6613b1_1280_720_base.png गुणन का अवकलन (Differentiating products) We explore the product rule by finding the derivative of eˣcos(x). We identify eˣ as the first function and cos(x) as the second, then apply the product rule to calculate the derivative, simplifying our result for a clearer understanding. https://cdn.kastatic.org/ka-youtube-converted/IgEHEIy8m80.mp4/IgEHEIy8m80.mp4 268 फलनों के अवकलजों का बीजगणित (Algebra of derivatives of functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:algebra-of-derivatives-of-functions/v/quotient-rule 2025-01-06T10:18:43.365910625Z भागफल नियम (Quotient rule) Discover the quotient rule, a powerful technique for finding the derivative of a function expressed as a quotient. We'll explore how to apply this rule by differentiating the numerator and denominator functions, and then combining them to simplify the result. video https://cdn.kastatic.org/ka_thumbnails_cache/c14f1e21-de50-4dc6-baec-a95ea5c0be20_1280_720_base.png भागफल नियम (Quotient rule) Discover the quotient rule, a powerful technique for finding the derivative of a function expressed as a quotient. We'll explore how to apply this rule by differentiating the numerator and denominator functions, and then combining them to simplify the result. https://cdn.kastatic.org/ka-youtube-converted/wHDunJepylY.mp4/wHDunJepylY.mp4 233 फलनों के अवकलजों का बीजगणित (Algebra of derivatives of functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:algebra-of-derivatives-of-functions/v/rational-functions-differentiation 2025-01-06T10:18:03.589731621Z परिमेय फलनों का अवकलन (Differentiating rational functions) Let's dive into the differentiation of the rational function (5-3x)/(x²+3x) using the Quotient Rule. By identifying the numerator and denominator as separate functions, we apply the Quotient Rule to find the derivative, simplifying the expression for a clear understanding of the process. This approach can be applied to differentiate any other rational function as well. video https://cdn.kastatic.org/ka_thumbnails_cache/2d6523b3-d609-48f7-9621-0b180a70fa94_1280_720_base.png परिमेय फलनों का अवकलन (Differentiating rational functions) Let's dive into the differentiation of the rational function (5-3x)/(x²+3x) using the Quotient Rule. By identifying the numerator and denominator as separate functions, we apply the Quotient Rule to find the derivative, simplifying the expression for a clear understanding of the process. This approach can be applied to differentiate any other rational function as well. https://cdn.kastatic.org/ka-youtube-converted/Ds2vDTPz9Q0.mp4/Ds2vDTPz9Q0.mp4 404 फलनों के अवकलजों का बीजगणित (Algebra of derivatives of functions)