By exploiting our knowledge of logarithms, we can make certain derivatives much smoother to compute. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-adv-derivatives-opt-vids/v/proof-of-derivative-of-ex?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-advanced/ab-diff-log/v/chain-rule-with-triple-composition?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=R2JsjJyr0ck Note: All Khan Academy content is available for free at (www.khanacademy.org)

Long video explaining why entropy is a measure of the number of states a system can take on (mathy, but mind-blowing). Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/science/physics/thermodynamics/laws-of-thermodynamics/v/entropy-intuition?utm_source=YT&utm_medium=Desc&utm_campaign=physics Missed the previous lesson? https://www.khanacademy.org/science/physics/thermodynamics/laws-of-thermodynamics/v/thermodynamic-entropy-definition-clarification?utm_source=YT&utm_medium=Desc&utm_campaign=physics Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry. 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=WLKEVfLFau4 Note: All Khan Academy content is available for free at (www.khanacademy.org)

Lindsay finds the measure of angle using addition. Practice this yourself on Khan Academy right now: https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-geometry-topic/4th-decomposing-angles/e/decomposing-angles Watch the next lesson: https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-geometry-topic/4th-decomposing-angles/v/decomposing-angles Missed the previous lesson? https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-geometry-topic/cc-4th-interpreting-angles/v/acute-right-and-obtuse-angles 4th grade math on Khan Academy: 4th grade is the time to start really fine-tuning your arithmetic skills. Not only will you be a multi-digit addition and subtraction rockstar, but you'll extend the multiplication and division that you started in 3rd grade to several digits. You'll also discover that you sometimes have something left over (called a "remainder") when you divide. In 3rd grade you learned what a fraction is. Now you'll start adding, subtracting, multiplying, and comparing them. You'll also see how they relate to decimals. On other fronts, you'll learn how to convert between different units (which is super important when comparing the size and speed of robot unicorns in different countries) and continue your journey thinking about various shapes in two dimensions. Some of the foundational concepts of geometry (like lines, rays and angles) also get introduced. As always, we'll round this out with a healthy dose of applied word problems and explorations of number patterns and properties (including the ideas of factors, multiples and prime numbers). The fun must not stop! (Content was selected for this grade level based on a typical curriculum in the United States.) ... https://www.youtube.com/watch?v=uMj46crbLaw Note: All Khan Academy content is available for free at (www.khanacademy.org)

Showing that the Null Space of a Matrix is a valid Subspace Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/null-space-2-calculating-the-null-space-of-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Missed the previous lesson? https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/matrix-vector-products?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. 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=jCwRV1QL_Xs Note: All Khan Academy content is available for free at (www.khanacademy.org)