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Calculus: Higher-Order Derivatives, Linear Approx In this lesson, we learn about multiple derivatives and tangent line approximations for these. Higher-order derivatives are results of taking the derivative more than once. Where the derivative of x^4 is 4x^3. The second derivative of the original x^4 would be the derivative of the derivative, which is 12x^2. You can also calculate third and fourth derivatives and so on... This lesson will walk you through what notation (Leibniz notation) denotes higher-order derivatives (d^2y/dx^2) or with multiple prime sympols for f(x) derivatives. Derivatives can allow you to approximate values of complicated functions near values you know. For example, in this video, you will see Professor Burger approximate the square root of 4.1 by using derivatives and the knowledge that the square root of 4 is equal to 2 (a very close point on the function's graph). Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'H?pital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics. Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College. He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America". Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions. Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Length: 02:54


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