How To Find the nth Derivative w/ Taylor & Maclaurin Series (Higher Derivatives)

Have you ever come across a calculus problem asking you to find the 100th derivative of a function? You might be wondering: Is there an nth derivative formula? Well, one of the more surprising applications of Taylor & Maclaurin series is finding higher derivatives. In this video, we'll see a quick trick for finding higher derivatives using Maclaurin & Taylor series and do an example problem to find the 94th derivative of ln(1 + x^2 / 3) at x=0. Download the Study Guide PDF: https://crambetter.com/pdfs/youtube/Taylor%20Series%20and%20Higher%20Derivatives%20Topic%20Review%20-%20YouTube.pdf Get the rest of the CramBetter Calculus 2 course: https://crambetter.com Video contents: 00:00 - Steps for Finding the nth Derivative 00:54 - Example Problem (94th Derivative of Natural Log) 01:30 - Step 1: Choosing a Known Maclaurin Series 02:08 - Step 2: Substitution 03:20 - Step 3: Making Sure the Derivative Doesn't Equal 0 04:04 - Step 4: Plugging in n to the Generic Power Series 05:02 - Step 5: Make Sure The Powers Match 06:28 - Final Answer #calculus #calculus2 #college ----- CramBetter is a 24/7 online study platform for college students. We give you a clear study guide for each topic in your course to go along with videos that make subjects like math, physics, and chemistry simpler to understand. We also help you test your knowledge with practice exam questions (and detailed video solutions if you get stuck!). Every tutor at CramBetter has a master’s degree or higher and 8+ years of teaching experience. We’ve worked as College Board AP instructors, university teaching assistants, and private tutors — helping tens of thousands of students stress less and pass their classes.