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Lambert W Function (domain, range, approximation, solving equations, derivative & integral)

Comparing the natural log function ln(x) and the product log function W(x). 0:00 ln(x) vs. W(x) 1. Solve e^x=2 & ln(2), 0:16 2. Solve xe^x=2 & W(2), 3:01 Newton's Method:    • Newton's method and Omega Constant   3. Domain, range, & graph for ln(x), 6:53 4. Domain, range, & graph for W(x), 9:16 5. Nice values for ln(x), 13:30 6. Nice values for W(x), 15:47 7. Solve e^x-e^(-x)=1, 19:54 8. Solve x+e^x=2, 22:40 9. Solve x^x=2, 25:25 (the t-shirt https://teespring.com/cute-math-cat-6) 10. Derivative of ln(x) by implicit differentiation, 27:30 11. Derivative of W(x) by implicit differentiation, 28:35 Integral of an inverse function, 32:50 12. Integral of ln(x) by the formula, 36:52 13. Integral of W(x) by the formula, 38:42 14. What's ln(i)? 43:50 15. What's W(-pi/2)? 46:11 Read more about the Lambert W function on Wikipedia: https://en.wikipedia.org/wiki/Lambert... 🔑 If you enjoy my videos, then you can click here to subscribe https://www.youtube.com/blackpenredpe... 🏬 Shop math t-shirt & hoodies: https://teespring.com/stores/blackpen... 10% off with the code "TEESPRINGWELCOME10" 😎 IG:   / blackpenredpen   ☀️ Twitter:   / blackpenredpen   Equipment: 👉 Expo Markers (black, red, blue): https://amzn.to/2T3ijqW 👉 The whiteboard: https://amzn.to/2R38KX7 👉 Ultimate Integrals On Your Wall: https://teespring.com/calc-2-integral... --------------------------------------------------------------------------------------------------- **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 --------------------------------------------------------------------------------------------------- 💪 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   Thank you, blackpenredpen