https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:derivatives/v/differentiating-polynomials-example 2025-01-06T10:18:43.365910625Z बहुपदों का अवकलन (Differentiating polynomials) Let's explore how to differentiate polynomials using the power rule and derivative properties. We work with the function f(x)=x⁵+2x³-x² and apply the power rule to find its derivative, f'(x)=5x⁴+6x²-2x. Next, we evaluate f'(x) at x=2, determining that f'(2)=100, which represents the rate of change or slope of the tangent line at the specified point. video https://cdn.kastatic.org/ka_thumbnails_cache/0733d876-f0c2-49a1-a06a-4553cc763424_1280_720_base.png बहुपदों का अवकलन (Differentiating polynomials) Let's explore how to differentiate polynomials using the power rule and derivative properties. We work with the function f(x)=x⁵+2x³-x² and apply the power rule to find its derivative, f'(x)=5x⁴+6x²-2x. Next, we evaluate f'(x) at x=2, determining that f'(2)=100, which represents the rate of change or slope of the tangent line at the specified point. https://cdn.kastatic.org/ka-youtube-converted/2w7TMXW_rvg.mp4/2w7TMXW_rvg.mp4 399 बहुपदीय और त्रिकोणमितीय फलनों के अवकलज (Derivative of polynomials and trigonometric functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivative-of-polynomials-and-trigonometric-functions/v/negative-powers-differentiation 2025-01-06T10:18:43.365910625Z पूर्णांक घातों का अवकलन (धनात्मक एवं ऋणात्मक) {Differentiating integer powers (mixed positive and negative)} Let's explore how to differentiate the function g(x) = 2/(x³) - 1/(x²) and evaluate the derivative at x = 2. By applying the Power Rule and simplifying, we efficiently find the slope of the tangent line at the given point. video https://cdn.kastatic.org/ka_thumbnails_cache/7a187983-2fd4-443c-8d47-54e201520872_1280_720_base.png पूर्णांक घातों का अवकलन (धनात्मक एवं ऋणात्मक) {Differentiating integer powers (mixed positive and negative)} Let's explore how to differentiate the function g(x) = 2/(x³) - 1/(x²) and evaluate the derivative at x = 2. By applying the Power Rule and simplifying, we efficiently find the slope of the tangent line at the given point. https://cdn.kastatic.org/ka-youtube-converted/fdKDWz9pKqA.mp4/fdKDWz9pKqA.mp4 289 बहुपदीय और त्रिकोणमितीय फलनों के अवकलज (Derivative of polynomials and trigonometric functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivative-of-polynomials-and-trigonometric-functions/v/derivatives-of-sinx-and-cosx 2025-01-06T10:18:43.365910625Z sin x और cos (x) के अवकलज (Derivatives of sin(x) and cos(x)) Now we explore the intuition behind the derivatives of trigonometric functions, discovering that the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x). By analyzing tangent line slopes, we gain a deeper understanding of these fundamental relationships. video https://cdn.kastatic.org/ka_thumbnails_cache/143d8bb3-355a-4530-8fee-a5d499d206f1_1280_720_base.png sin x और cos (x) के अवकलज (Derivatives of sin(x) and cos(x)) Now we explore the intuition behind the derivatives of trigonometric functions, discovering that the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x). By analyzing tangent line slopes, we gain a deeper understanding of these fundamental relationships. https://cdn.kastatic.org/ka-youtube-converted/xCPbwScBqHc.mp4/xCPbwScBqHc.mp4 221 बहुपदीय और त्रिकोणमितीय फलनों के अवकलज (Derivative of polynomials and trigonometric functions) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:basic-calculus/x09646558c1ff0797:derivatives/v/sine-and-cosine-differentiation 2025-01-06T10:18:43.365910625Z sin(x) और cos(x)के अवकलज:उदहारण (worked example:Derivatives of sin(x) and cos(x)) Dive into the derivative of the function g(x) = 7sin(x) - 3cos(x) - (π/∛x)². By applying the power rule and the derivatives of sine and cosine functions, we efficiently determine the derivative g'(x) = 7cos(x) + 3sin(x) + 2π²/3 * x^(-5/3). Through algebraic manipulation and careful attention to detail, we tackle the problem's initially intimidating appearance. video https://cdn.kastatic.org/ka_thumbnails_cache/8ceec945-79e9-4fb2-87fc-be0e3e17ff4a_1280_720_base.png sin(x) और cos(x)के अवकलज:उदहारण (worked example:Derivatives of sin(x) and cos(x)) Dive into the derivative of the function g(x) = 7sin(x) - 3cos(x) - (π/∛x)². By applying the power rule and the derivatives of sine and cosine functions, we efficiently determine the derivative g'(x) = 7cos(x) + 3sin(x) + 2π²/3 * x^(-5/3). Through algebraic manipulation and careful attention to detail, we tackle the problem's initially intimidating appearance. https://cdn.kastatic.org/ka-youtube-converted/EBZQ57X657U.mp4/EBZQ57X657U.mp4 314 बहुपदीय और त्रिकोणमितीय फलनों के अवकलज (Derivative of polynomials and trigonometric functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivative-of-polynomials-and-trigonometric-functions/v/derivatives-of-tanx-and-cotx 2025-01-06T10:18:03.589731621Z tan(x) और cot(x) के अवकलज (Derivatives of tan(x) and cot(x)) We find the derivatives of tan(x) and cot(x) by rewriting them as quotients of sin(x) and cos(x). Using the quotient rule, we determine that the derivative of tan(x) is sec^2(x) and the derivative of cot(x) is -csc^2(x). This process involves applying the Pythagorean identity to simplify final results. video https://cdn.kastatic.org/ka_thumbnails_cache/398fc34d-7f9d-477b-a994-1d426b066ef9_1280_720_base.png tan(x) और cot(x) के अवकलज (Derivatives of tan(x) and cot(x)) We find the derivatives of tan(x) and cot(x) by rewriting them as quotients of sin(x) and cos(x). Using the quotient rule, we determine that the derivative of tan(x) is sec^2(x) and the derivative of cot(x) is -csc^2(x). This process involves applying the Pythagorean identity to simplify final results. https://cdn.kastatic.org/ka-youtube-converted/WmCRLnWbIKc.mp4/WmCRLnWbIKc.mp4 278 बहुपदीय और त्रिकोणमितीय फलनों के अवकलज (Derivative of polynomials and trigonometric functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivative-of-polynomials-and-trigonometric-functions/v/derivatives-of-secx-and-cscx 2025-01-06T10:18:03.589731621Z sec(x) और csc(x) के अवकलज (Derivatives of sec(x) and cosec(x)) Let's explore the derivatives of sec(x) and csc(x) by expressing them as 1/cos(x) and 1/sin(x), respectively, and applying the quotient rule. We discover that the derivative of sec(x) can be written as sin(x)/cos²(x) or tan(x)sec(x), and the derivative of csc(x) can be expressed as -cos(x)/sin²(x) or -cot(x)csc(x). video https://cdn.kastatic.org/ka_thumbnails_cache/71aa4205-5f9b-457e-b9f4-29e95f3e932b_1280_720_base.png sec(x) और csc(x) के अवकलज (Derivatives of sec(x) and cosec(x)) Let's explore the derivatives of sec(x) and csc(x) by expressing them as 1/cos(x) and 1/sin(x), respectively, and applying the quotient rule. We discover that the derivative of sec(x) can be written as sin(x)/cos²(x) or tan(x)sec(x), and the derivative of csc(x) can be expressed as -cos(x)/sin²(x) or -cot(x)csc(x). https://cdn.kastatic.org/ka-youtube-converted/ZzgWmFWfYg4.mp4/ZzgWmFWfYg4.mp4 268 बहुपदीय और त्रिकोणमितीय फलनों के अवकलज (Derivative of polynomials and trigonometric functions) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:limits-and-derivatives-ncert-new/x808831787a7b08a2:derivative-of-polynomials-and-trigonometric-functions/v/derivatives-of-trigonometric-functions 2025-06-25T04:36:24.163902917Z त्रिकोणमितीय फलनों के अवकलज In this video, we'll practice applying product and quotient rules of differentiation on trigonometric functions. We'll first do a quick refresher on both of these rules and then solve two problems each for both rules. We'll also look at one bonus rule that we'll study in grade 12th called the chain rule. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw त्रिकोणमितीय फलनों के अवकलज In this video, we'll practice applying product and quotient rules of differentiation on trigonometric functions. We'll first do a quick refresher on both of these rules and then solve two problems each for both rules. We'll also look at one bonus rule that we'll study in grade 12th called the chain rule. https://cdn.kastatic.org/ka-youtube-converted/R5fbBrqpNu4.mp4/R5fbBrqpNu4.mp4 452 बहुपदीय और त्रिकोणमितीय फलनों के अवकलज (Derivative of polynomials and trigonometric functions)