Introduction to the gradient Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/partial_derivatives_topic/gradient/v/gradient-of-a-scalar-field?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus Missed the previous lesson? https://www.khanacademy.org/math/multivariable-calculus/partial_derivatives_topic/partial_derivatives/v/partial-derivatives-2?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. ... https://www.youtube.com/watch?v=U7HQ_G_N6vo

Parts 2b and 2c of the 2008 BC exam (free response). Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2008/v/calculus-bc-2008-2d?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-solved-exams/bc-solved-exams-2008/v/calculus-bc-2008-2-a?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. ... https://www.youtube.com/watch?v=S4oOSgTj9C8

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/applying-math-reasoning-topic/alternate-number-bases/v/binary-to-hexadecimal?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Missed the previous lesson? https://www.khanacademy.org/math/pre-algebra/applying-math-reasoning-topic/alternate-number-bases/v/binary-addition?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off! About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything ... https://www.youtube.com/watch?v=xHWKYFhhtJQ Note: All Khan Academy content is available for free at (www.khanacademy.org)

A deep dive into the Eighth Amendment, which protects citizens from excessive fines and cruel and unusual punishment. In this video, Kim discusses the Eighth Amendment with scholars John Bessler and John Stinneford. To read more about the Eighth Amendment, visit the National Constitution Center’s Interactive Constitution. On this site, leading scholars interact and explore the Constitution and its history. For each provision of the Constitution, experts from different political perspectives coauthor interpretive explanations when they agree and write separately when their opinions diverge. View more lessons or practice this subject at https://www.khanacademy.org/humanities/ap-us-government-and-politics/civil-liberties-and-civil-rights/amendments-balancing-individual-freedom-with-public-order-and-safety/v/the-eighth-amendment?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc ... https://www.youtube.com/watch?v=i2ewIPvsWpo Note: All Khan Academy content is available for free at (www.khanacademy.org)