https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/x2dd7feea:differentiation-definition-and-basic-derivative-rules-free-response-questions/a/differentiation-definition-and-fundamental-properties-frqs 2026-06-25T15:40:55.094699315Z Differentiation: definition and fundamental properties FRQs What types of questions focus on concepts from multiple units? What makes a high-quality response? How are the responses scored? This article walks you through these questions. article https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/x2dd7feea:differentiation-definition-and-basic-derivative-rules-free-response-questions/v/estimating-rate-of-change-2011-ap-calculus-ab-free-response-2a 2026-06-29T20:40:47.259641521Z Estimating rate of change 2011 AP Calculus AB free response 2a Estimating rate of change using a table. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/859857ea-6660-4e82-91dc-eb9353f85414_1280_720_base.png Estimating rate of change 2011 AP Calculus AB free response 2a Estimating rate of change using a table. https://cdn.kastatic.org/ka-youtube-converted/gXVKbTwricA.mp4/gXVKbTwricA.mp4 216 Free response questions: differentiation definition and basic derivative rules https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/x2dd7feea:differentiation-definition-and-basic-derivative-rules-free-response-questions/v/writing-equation-of-tangent-line-ap-calculus-ab-free-response-2011-3a 2026-06-29T20:40:47.259641521Z Writing equation of tangent line AP Calculus AB free response 2011 3a Writing the equation of a tangent line given a function and an x-value. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/6e804c29-30a2-4de4-9b80-affd31dc487b_1280_720_base.png Writing equation of tangent line AP Calculus AB free response 2011 3a Writing the equation of a tangent line given a function and an x-value. https://cdn.kastatic.org/ka-youtube-converted/-KaohGMliAU.mp4/-KaohGMliAU.mp4 179 Free response questions: differentiation definition and basic derivative rules https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/x2dd7feea:differentiation-definition-and-basic-derivative-rules-free-response-questions/v/2015-ap-calculus-abbc-3a 2026-06-29T20:40:47.259641521Z Estimating rate of change: 2015 AP Calculus AB/BC 3a Estimating acceleration video https://cdn.kastatic.org/googleusercontent/Gh0WWixcVOjX6RK1wXjUDgZ2PraiLLlmM2b_Sz5Sz_LV0bRLNPE2syWPMmMYr3AO86GnaAk0xjzK_RM15F0wKaQf Estimating rate of change: 2015 AP Calculus AB/BC 3a Estimating acceleration https://cdn.kastatic.org/ka-youtube-converted/sdFT_8AJsy0.mp4/sdFT_8AJsy0.mp4 349 Free response questions: differentiation definition and basic derivative rules https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/x2dd7feea:differentiation-definition-and-basic-derivative-rules-free-response-questions/v/2015-ap-calculus-ab-6a 2026-06-29T20:40:47.259641521Z Writing equation of tangent line: 2015 AP Calculus AB 6a Equation for tangent line video https://cdn.kastatic.org/googleusercontent/LnHB6Z7b3GyFXAoMNwX25C3G5D4f52enNYgWlJFTxK-_v_QzjaNrexefqzKJSsSMNl3BWE7G5oPTFqr0lEk0ERc Writing equation of tangent line: 2015 AP Calculus AB 6a Equation for tangent line https://cdn.kastatic.org/ka-youtube-converted/4ThUMRAvUkY.mp4/4ThUMRAvUkY.mp4 148 Free response questions: differentiation definition and basic derivative rules https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/x2dd7feea:differentiation-definition-and-basic-derivative-rules-free-response-questions/v/using-average-rate-of-change-and-first-derivative-2018-calculus-ab-free-response-5ab 2026-06-25T15:40:55.094699315Z Using average rate of change and first derivative, 2018 Calculus AB free response 5a,b Calculate the average rate of change on an interval, determine the equation for the first derivative using the product rule, and use the first derivative to determine the slope of a line tangent to a graph at a given point, 2018 Calculus AB free response 5a,b. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/e45ca8c4-43bb-4e22-a1ce-7658840053e0_1280_720_base.png Using average rate of change and first derivative, 2018 Calculus AB free response 5a,b Calculate the average rate of change on an interval, determine the equation for the first derivative using the product rule, and use the first derivative to determine the slope of a line tangent to a graph at a given point, 2018 Calculus AB free response 5a,b. https://cdn.kastatic.org/ka-youtube-converted/zXfGK-Eh4c0.mp4/zXfGK-Eh4c0.mp4 233 Free response questions: differentiation definition and basic derivative rules https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/x2dd7feea:differentiation-definition-and-basic-derivative-rules-free-response-questions/v/relating-derivative-to-tangent-line-2019-calculus-ab-free-response-6ab 2026-06-25T15:40:55.094699315Z Relating derivative to tangent line, 2019 Calculus AB free response 6a,b The relationship between the value of the first derivative of a function at a point and the slope of the tangent line, and how to use the product rule, 2019 Calculus AB free response 6a,b. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/1f99bea9-20e7-4328-872e-eccc02cccdb9_1280_720_base.png Relating derivative to tangent line, 2019 Calculus AB free response 6a,b The relationship between the value of the first derivative of a function at a point and the slope of the tangent line, and how to use the product rule, 2019 Calculus AB free response 6a,b. https://cdn.kastatic.org/ka-youtube-converted/w_hXTuSwNJ4.mp4/w_hXTuSwNJ4.mp4 252 Free response questions: differentiation definition and basic derivative rules https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/x2dd7feea:differentiation-definition-and-basic-derivative-rules-free-response-questions/v/determining-when-first-derivative-equals-average-rate-of-change-2025-calculus-ab-free-response-1b 2026-06-25T15:40:55.094699315Z Determining when first derivative equals average rate of change, 2025 Calculus AB free response 1b Calculate the average rate of change, and the relationship between the first derivative and instantaneous rate of change, 2025 Calculus AB free response 1b. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/0266db00-42df-4c1a-9d37-5c9ac8d1583e_1280_720_base.png Determining when first derivative equals average rate of change, 2025 Calculus AB free response 1b Calculate the average rate of change, and the relationship between the first derivative and instantaneous rate of change, 2025 Calculus AB free response 1b. https://cdn.kastatic.org/ka-youtube-converted/HDwfKnZ5A2U.mp4/HDwfKnZ5A2U.mp4 427 Free response questions: differentiation definition and basic derivative rules