This is the simplest case of taking the derivative of a composition involving multivariable functions.

Discriminant for Types of Solutions for a Quadratic Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/e/solutions_to_quadratic_equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_ineq/v/quadratic-inequalities?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Missed the previous lesson? https://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/v/discriminant-of-quadratic-equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2…

How haploid gametes (sperm and egg cells) combine to form a diploid zygote with two sets of chromosomes. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/test-prep/mcat/cells/cellular-division/v/somatic-germ-cells?utm_source=YT&utm_medium=Desc&utm_campaign=mcat Missed the previous lesson? https://www.khanacademy.org/test-prep/mcat/cells/cellular-division/v/loss-of-cell-cycle-control-in-cancer?utm_source=YT&utm_medium=Desc&utm_campaign=mcat MCAT on Khan Academy: Go ahead and practice some passage-based questions! About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a…

World War II, Hitler, Cold War, Bay of Pigs, Cuban Missile Crisis and the Space Race More free lessons at: http://www.khanacademy.org/video?v=j2eKaxU-8kA

Learn how to classify numbers as whole numbers, integers, rational numbers, and irrational numbers. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-irrational-numbers/e/identifying-whole–integer–and-rational-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=8thgrade Watch the next lesson: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-approximating-irrational-numbers/v/approximating-square-roots-2?utm_source=YT&utm_medium=Desc&utm_campaign=8thgrade Missed the previous lesson? https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-irrational-numbers/v/recognizing-irrational-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=8thgrade 8th grade on Khan Academy: 8th grade is all about tackling the meat of algebra and getting exposure to some of the…

Not only will we identify several absolute values in this example, but we will order them from smallest to largest. Content provided by The NROC Project – ©Monterey Institute for Technology and Education Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/arithmetic/absolute-value/abs_value_tutorial/e/absolute_value?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Watch the next lesson: https://www.khanacademy.org/math/arithmetic/absolute-value/abs_value_tutorial/v/absolute-value-of-integers?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Missed the previous lesson? https://www.khanacademy.org/math/arithmetic/absolute-value/abs_value_tutorial/v/absolute-value-and-number-lines?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Pre-Algebra on Khan…

Mitosis is how cells divide! Learn what happens in all the phases of mitosis: prophase, metaphase, anaphase, and telophase. Watch the next lesson: https://www.khanacademy.org/test-prep/mcat/cells/cellular-division/v/comparing-mitosis-and-meiosis?utm_source=YT&utm_medium=Desc&utm_campaign=mcat Missed the previous lesson? https://www.khanacademy.org/test-prep/mcat/cells/cellular-division/v/interphase?utm_source=YT&utm_medium=Desc&utm_campaign=mcat MCAT on Khan Academy: Go ahead and practice some passage-based questions! About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard…

Solving for a Variable 2 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/e/solving_for_a_variable?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/v/example-of-solving-for-a-variable?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Missed the previous lesson? https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/v/solving-for-a-variable?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and…

Using the monotonicity theorem to determine when a function is increasing or decreasing.

Starting to apply Stokes theorem to solve a line integral Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/surface-integrals/stokes_theorem/v/part-2-parameterizing-the-surface?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus Missed the previous lesson? https://www.khanacademy.org/math/multivariable-calculus/surface-integrals/stokes_theorem/v/conditions-for-stokes-theorem?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…

In March 2016, the SAT is switching to a new format. Sal covers how the exam is changing. Watch the next lesson: https://www.khanacademy.org/test-prep/new-sat/new-sat-tips-planning/new-sat-about-sat/v/sat-differences-of-new-sat?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT Missed the previous lesson? https://www.khanacademy.org/test-prep/new-sat/new-sat-tips-planning/new-sat-about-sat/v/walk-through-sat-practice-platform?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT New SAT (starting March 2016) on Khan Academy: Practice all of the skills you’ll need for the new SAT. We also have four official practice exams from…

Looking at marginal and average total cost in the context of a juice business Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/firm-economic-profit/average-costs-margin-rev/v/marginal-revenue-and-marginal-cost?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/microeconomics/firm-economic-profit/economic-profit-tutorial/v/depreciation-and-opportunity-cost-of-capital?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics Microeconomics on Khan Academy: Topics covered in a traditional college level introductory microeconomics course About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower…

Naming cations, anions, and simple ionic compounds such as potassium chloride. View more lessons or practice this subject at https://www.khanacademy.org/science/chemistry/atomic-structure-and-properties/introduction-to-compounds/v/naming-ions-and-ionic-compounds?utm_source=youtube&utm_medium=desc&utm_campaign=chemistry 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,…

Thinking about when oligopolies behave more like monopolies or perfect competitors Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/microeconomics/nash-equilibrium-tutorial/nash-eq-tutorial/v/prisoners-dilemma-and-nash-equilibrium?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics Missed the previous lesson? https://www.khanacademy.org/economics-finance-domain/microeconomics/perfect-competition-topic/monopolistic-competition-oligop/v/monopolistic-competition-and-economic-profit?utm_source=YT&utm_medium=Desc&utm_campaign=microeconomics Microeconomics on Khan Academy: Topics covered in a traditional college level introductory microeconomics course About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study…

How can we tell if a sequence converges or diverges? See Sal in action, determining the convergence/divergence of several sequences. Created by Sal Khan. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-inf-sequences/e/convergence-and-divergence-of-sequences?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-finite-geo-series/v/series-as-sum-of-sequence?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-inf-sequences/v/convergent-and-divergent-sequences?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC AP Calculus BC on Khan Academy: Learn AP Calculus BC – everything…

Option Expiration and Price. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/forward-contract-introduction?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/put-call-options/v/actual-option-quotes?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Finance and capital markets on Khan Academy: Options allow investors and speculators to hedge downside (or upside). It allows them to trade on a belief that prices will change a lot–just not clear about direction.…

Number Sets Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/number-sets-pre-alg/v/number-sets-1?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra Missed the previous lesson? https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/div-fractions-fractions-pre-alg/v/examples-of-dividing-negative-fractions?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…

Correction – 2-Propylheptane should never be the name! Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/science/organic-chemistry/bond-line-structures-alkanes-cycloalkanes/naming-alkanes/v/common-and-systematic-naming-iso-sec-and-tert-prefixes?utm_source=YT&utm_medium=Desc&utm_campaign=organicchemistry Missed the previous lesson? https://www.khanacademy.org/science/organic-chemistry/bond-line-structures-alkanes-cycloalkanes/naming-alkanes/v/naming-alkanes-with-alkyl-groups?utm_source=YT&utm_medium=Desc&utm_campaign=organicchemistry Organic Chemistry on Khan Academy: Carbon can form covalent bonds with itself and other elements to create a mind-boggling array of structures. In organic chemistry, we will learn about the reactions chemists use…

Analysis of Variance 1 – Calculating SST (Total Sum of Squares) Watch the next lesson: https://www.khanacademy.org/math/probability/statistics-inferential/anova/v/anova-2-calculating-ssw-and-ssb-total-sum-of-squares-within-and-between-avi?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/contingency-table-chi-square-test?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go…

A subject is the noun phrase that drives the action of a sentence; in the sentence “Jake ate cereal,” Jake is the subject. The direct object is the thing that the subject acts upon, so in that last sentence, “cereal” is the direct object; it’s the thing Jake ate. An indirect object is an optional…

We’re proud to announce we’ll soon offer free, personalized LSAT prep for all. Every year, more than 100,000 people take the LSAT, the Law School Admission Test. Many test takers have traditionally paid for test prep, which can cost hundreds or even thousands of dollars. We’re excited to offer a free LSAT practice program designed…

The perfect cipher Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/frequency-stability?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/polyalphabetic-cipher?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Computer Science on Khan Academy: Learn select topics from computer science – algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress…

Independent realization from an ancestor’s perspective Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-1?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/random-vs-pseudorandom-number-generators?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience Computer Science on Khan Academy: Learn select topics from computer science – algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we…

Biology overview

Expensing a truck leads to strange looking income statement. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/core-finance/accounting-and-financial-stateme/depreciation-amortization-tut/v/depreciating-the-truck?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Missed the previous lesson? Watch here: https://www.khanacademy.org/economics-finance-domain/core-finance/accounting-and-financial-stateme/financial-statements-tutorial/v/fair-value-accounting?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Finance and capital markets on Khan Academy: How do you account for things that get “used up” or a cost that should be spread over time. This tutorial has your…

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra2/functions_and_graphs/function_expressions/e/functions_2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Watch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/function_expressions/v/difference-of-functions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Missed the previous lesson? https://www.khanacademy.org/math/algebra2/functions_and_graphs/function-introduction/v/understanding-function-notation-example-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only…

Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/humanities/world-history/euro-hist/world-war-i-fighting/v/comparing-the-eastern-and-western-fronts-in-wwi?utm_source=YT&utm_medium=Desc&utm_campaign=worldhistory Missed the previous lesson? https://www.khanacademy.org/humanities/world-history/euro-hist/american-entry-world-war-i/v/united-states-enters-world-war-i?utm_source=YT&utm_medium=Desc&utm_campaign=worldhistory World history on Khan Academy: From the earliest civilizations to the modern world, geography, religion, trade, and politics have bound peoples and nations together — and torn them apart. Take a journey through time and space and discover the fascinating history…