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Why is the derivative of e^x equal to e^x?

What's the number e and why is the derivative of e^x = e^x? Take a course from Brilliant to learn more about calculus 👉 https://brilliant.org/blackpenredpen/ (20% off with this link) In this video, we will learn the derivatives of exponential functions and we will see how we can define the number e. Calculus 1, AP calculus, calculus A-level lesson. For more math for fun videos like this, be sure to subscribe 👉 https://bit.ly/3o2fMNo 0:00 We will talk about why the derivative of e to the x is e to the x 0:30 Derivative of 2^x by the definition of derivative 3:43 Defining the number e 8:07 Differentiate b^x 9:52 Check out Brilliant 10:51 Bonus: derivative of ln(x) --------------------------------------------------------------------------------------------------- **Thanks to ALL my lovely patrons for supporting my channel and believing in what I do** AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff Julian Moik Hiu Fung Lam Ronald Bryant Jan Řehák Robert Toltowicz Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta --------------------------------------------------------------------------------------------------- 💪 If you would also like to support this channel and have your name in the video description, then you could become my patron here   / blackpenredpen   Batty McFaddin - Silent Film Light by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/... Source: http://incompetech.com/music/royalty-... Artist: http://incompetech.com/