The chain rule states that the derivative of f(g(x)) is f'(g(x))_g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x_) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x_. Using the chain rule and the derivatives of sin(x) and x_, we can then find the derivative of sin(x_). Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-chain-rule/v/recognizing-compositions-of-functions?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-rational-func-diff/v/linear-approximation-example?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago. 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=0T0QrHO56qg Note: All Khan Academy content is available for free at (www.khanacademy.org)

The difference between investment and consumption. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/investment-vs-consumption-2?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/investment-vehicles-tutorial/investment-consumption/v/return-on-capital?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Finance and capital markets on Khan Academy: When are you using capital to create more things (investment) vs. for consumption (we all need to consume a bit to be happy). When you do invest, how do you compare risk to return? Can capital include human abilities? This tutorial hodge-podge covers it all. 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=rEiLOB4FulY Note: All Khan Academy content is available for free at (www.khanacademy.org)

Carbon 14 Dating 2. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/measuring-age-tutorial/v/potassium-argon-k-ar-dating?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy Missed the previous lesson? https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/measuring-age-tutorial/v/carbon-14-dating-1?utm_source=YT&utm_medium=Desc&utm_campaign=cosmologystronomy Cosmology & Astronomy on Khan Academy: The Earth is huge, but it is tiny compared to the Sun (which is super huge). But the Sun is tiny compared to the solar system which is tiny compared to the distance to the next star. Oh, did we mention that there are over 100 billion stars in our galaxy (which is about 100,000 light years in diameter) which is one of hundreds of billions of galaxies in just the observable universe (which might be infinite for all we know). Don't feel small. We find it liberating. Your everyday human stresses are nothing compared to this enormity that we are a part of. Enjoy the fact that we get to be part of this vastness! 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=4YUtnod-YuE Note: All Khan Academy content is available for free at (www.khanacademy.org)

By combining stoichiometric calculations with the ideal gas law, we can calculate amounts of reactants and products for chemical reactions involving gases. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:chemical-reactions/x2eef969c74e0d802:stoichiometry/v/worked-example-relating-reaction-stoichiometry-and-the-ideal-gas-law 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 Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc ... https://www.youtube.com/watch?v=FRNTJmqMko8 Note: All Khan Academy content is available for free at (www.khanacademy.org)