my all-in-one calculus question

Want to learn more about calculus limits, derivatives, integrals, and infinite series? If so, head to Brilliant https://brilliant.org/blackpenredpen/ (20% off with this link)

This all-in-one calculus question contains the limit definition of derivative for f(x)=x^3 (aka the first principle for derivative), the power series of -ln(1-x) by integrating the best friend (aka the geometric series), the improper integral of ln(t) from 0 to x by using integration by parts (DI method) and using L'Hopital's rule to check the limit of t*ln(t) as t goes to 0+, and all the differentiation techniques (namely quotient rule, product rule, chain rule, power rule) to differentiate this monster! Enjoy!!! #calculus #blackpenredpen

0:00 my all-in-one calculus question
0:23 limit definition of derivative of the function f(x)=x^3
1:29 power series of -ln(1-x)
3:12 integral of ln(x) with integration by parts
6:28 differentiate this monster!
13:04 check out Brilliant
14:00 (bonus part) how I came up with this problem
Another all-in-one calculus question: 👉    • my all-in-one calculus question (uncut)  

For more math for fun videos like this, be sure to subscribe 👉 https://bit.ly/3o2fMNo

If you need more help with your class, check out my just calculus tutorial channel:    / justcalculus  

💪 Join our channel membership to unlock special perks,: https://bit.ly/34PGH4h
📸 Math notes on my Instagram:   / blackpenredpen  
🛍 Shop math t-shirt & hoodies: http://bit.ly/bprpmerch
10% off with the code "WELCOME10"

Equipment:
👉 Expo Markers (black, red, blue): https://amzn.to/3yYLqOf
👉 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 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 Troy R Katy Lap C Niltiac, Stealer of Souls
---------------------------------------------------------------------------------------------------
💪 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