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.

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

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[fynnch]

only vid that helped me for this problem thnx

[incizor]

This was really awesome! I learned loads, thank you!