https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6a/v/derivative-properties-and-polynomial-derivatives 2023-07-27T01:47:53.920337803Z 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 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/mzOBlH32qdk.mp4/mzOBlH32qdk.mp4 593 Algebra of derivatives of functions https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6a/v/differentiating-linear-functions 2023-07-27T01:47:53.920337803Z 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 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/4l_IvxXD9o8.mp4/4l_IvxXD9o8.mp4 286 Algebra of derivatives of functions https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6a/e/differentiating-linear-functions 2025-03-01T15:52:37.13987578Z Basic derivative rules: find the error Analyze solutions for finding the derivatives of linear functions using basic differentiation rules. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-6a/e/basic-differentiation-rules 2021-04-29T07:58:24Z Basic derivative rules: table Use basic differentiation rules to evaluate derivatives of combined functions. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-8/v/applying-the-product-rule-for-derivatives 2023-07-27T01:47:53.920337803Z 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 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/79ngr0Bur38.mp4/79ngr0Bur38.mp4 160 Algebra of derivatives of functions https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-8/v/differentiating-products 2023-07-27T01:47:53.920337803Z 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 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/WxTrxxW0qeM.mp4/WxTrxxW0qeM.mp4 268 Algebra of derivatives of functions https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-8/e/differentiate-products 2025-03-01T15:52:37.13987578Z Differentiate products Find the derivatives of products of basic functions. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-9/v/quotient-rule 2023-07-27T01:47:53.920337803Z 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 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/WqzY3xibFL8.mp4/WqzY3xibFL8.mp4 233 Algebra of derivatives of functions https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-9/e/differentiate-quotients 2025-03-01T15:52:37.13987578Z Differentiate quotients Find the derivatives of quotients of basic functions. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-9/v/rational-functions-differentiation 2023-07-27T01:47:53.920337803Z 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 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/wjm5ZYZ4hj8.mp4/wjm5ZYZ4hj8.mp4 404 Algebra of derivatives of functions https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-9/e/differentiate-rational-functions 2025-03-01T15:52:37.13987578Z Differentiate rational functions Find and evaluate derivatives of rational functions. Tomer Gal exercise