https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-4/v/rates-of-change-between-radius-and-area-of-circle 2024-01-26T05:27:08.622526922Z Related rates intro Join us as we explore the intriguing relationship between the rate at which a circle's radius expands and the corresponding rate of area growth. Using the tools of calculus, specifically derivatives, we'll tackle this concept, providing a practical application to real-world problems involving rates of change. This understanding forms a key part of mastering calculus and its applications. Sal Khan video https://cdn.kastatic.org/googleusercontent/bQ-Xg-7dlpXWZWvl8wS26KcRJV-wsqrLVdeviiFwgfczj3CR9LRPYIAWtiFl-zvNoi2gf1IplIPyG3dSNjWtitSorg Related rates intro Join us as we explore the intriguing relationship between the rate at which a circle's radius expands and the corresponding rate of area growth. Using the tools of calculus, specifically derivatives, we'll tackle this concept, providing a practical application to real-world problems involving rates of change. This understanding forms a key part of mastering calculus and its applications. https://cdn.kastatic.org/ka-youtube-converted/kQF9pOqmS0U.mp4/kQF9pOqmS0U.mp4 463 Rate of change of quantities https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-5/e/related-rates 2025-05-05T08:14:25.350149109Z Related rates intro Practice your understanding of related rates. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-5/e/related-rates-multiple-rates 2025-05-05T08:14:25.350149109Z Related rates (multiple rates) Solve related rates problems that involve three related quantities or more. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-3/v/derivative-and-marginal-cost 2024-01-26T05:27:08.622526922Z Marginal cost & differential calculus Through the lens of economics, we examine how the derivative can be used as a tool to understand marginal cost. We'll use a factory scenario to see how cost changes with quantity, and how this insight informs production decisions. Calculus—in real life! Sal Khan video https://cdn.kastatic.org/googleusercontent/Nn4Em0Ense_JolbZT7Jr8eNfJMf9bkhwKm88zEQ4Zdu_EwyYSdthMFibtSGE5y9YA_kxC-zFoHaE_YnLcq4_B8rf Marginal cost & differential calculus Through the lens of economics, we examine how the derivative can be used as a tool to understand marginal cost. We'll use a factory scenario to see how cost changes with quantity, and how this insight informs production decisions. Calculus—in real life! https://cdn.kastatic.org/ka-youtube-converted/Wkjz1LlX1CQ.mp4/Wkjz1LlX1CQ.mp4 280 Rate of change of quantities https://www.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:applications-of-derivatives/e/marginal-cost-and-marginal-revenue 2025-08-08T02:45:51.78671331Z Marginal cost and marginal revenue Marginal cost and marginal revenue Ashish Gupta exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-5/v/falling-ladder-related-rates 2024-01-26T05:27:08.622526922Z Related rates: Falling ladder Let's explore a thrilling real-world scenario in this video: a ladder slipping away from a wall! We'll use related rates to calculate how fast the top of the ladder falls. It's a fun and practical application of calculus that'll keep us on our toes. Sal Khan video https://cdn.kastatic.org/googleusercontent/DNFQ7QloKaiUeoJFJZ-y5mhNNLI5qnbmUiIvlJQqcYiT0HvSmEQi1SiHFFz7OsT8JoGuPR9r3apQsxyrDg1tP0DCuA Related rates: Falling ladder Let's explore a thrilling real-world scenario in this video: a ladder slipping away from a wall! We'll use related rates to calculate how fast the top of the ladder falls. It's a fun and practical application of calculus that'll keep us on our toes. https://cdn.kastatic.org/ka-youtube-converted/kBVDSu7v8os.mp4/kBVDSu7v8os.mp4 349 Rate of change of quantities https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-5/e/related-rates-pythagorean-theorem 2025-05-05T08:14:25.350149109Z Related rates (Pythagorean theorem) Solve related rates problem using the Pythagoream theorem. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-5/v/related-rates-of-water-pouring-into-cone 2024-01-26T05:27:08.622526922Z Related rates: water pouring into a cone In this video, we explore an intriguing scenario where we pour water into a cone-shaped cup at a constant rate. We'll discover how the rate of change in the water's depth connects to the rate of change in volume, all with the help of our new related rates tools. Sal Khan video https://cdn.kastatic.org/googleusercontent/op-eE7U0NN3kobv4HYSR3VDH2upLb8_q15M_4RNAA9sLjKUrSxa1IWQcUci-7-QrLqNAjN7HeFhHDqTcftXukbXB Related rates: water pouring into a cone In this video, we explore an intriguing scenario where we pour water into a cone-shaped cup at a constant rate. We'll discover how the rate of change in the water's depth connects to the rate of change in volume, all with the help of our new related rates tools. https://cdn.kastatic.org/ka-youtube-converted/Xe6YlrCgkIo.mp4/Xe6YlrCgkIo.mp4 692 Rate of change of quantities https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-5/v/rate-of-change-of-balloon-height 2024-01-26T05:27:08.622526922Z Related rates: balloon Let's imagine we're at a hot air balloon show, and we're tracking a balloon's ascent. Using our knowledge of angles, distances, and related rates we can apply trigonometry and calculus to find the rate of change in the balloon's height. Sal Khan video https://cdn.kastatic.org/googleusercontent/jlbLIgkgGigMX3tJL9Y8brGLqMfcTFOt8PZ4jUbr1WHtjNTMBZhFxCylXCZokZ1TS13u13CsF83v5vVHczzTDFcd Related rates: balloon Let's imagine we're at a hot air balloon show, and we're tracking a balloon's ascent. Using our knowledge of angles, distances, and related rates we can apply trigonometry and calculus to find the rate of change in the balloon's height. https://cdn.kastatic.org/ka-youtube-converted/_kbd6troMgA.mp4/_kbd6troMgA.mp4 497 Rate of change of quantities https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-new/ab-4-5/e/related-rates-advanced 2025-05-05T08:14:25.350149109Z Related rates (advanced) Solve more elaborate problems with related rates. Tomer Gal exercise