In this video I go over Problem 1 which asks us to determine the 15th derivative at x = 0 for the function sin(x^3). Instead of manually solving the derivatives one by one, we can instead use the Maclaurin series for sin(x), replace x with x^3, and then solve for the 15th derivative for the corresponding series coefficient.
The timestamps of key parts of the video are listed below:
- Problem 1: 15th Derivative of sin(x^3) at x = 0: 0:00
- Maclaurin Series for sin(x): 0:40
- Derivatives as Series Coefficients: 3:30
- Calculation Check: 5:06
This video was taken from my earlier video listed below:
- Infinite Sequences and Series: Problems Plus:
- HIVE video notes: @mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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