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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: 👉 https://youtu.be/3s1WYUWYEKU

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