【詳細解題動畫】提要227：已知 f = 1/√(x² + y² + z²)，在 P: (1,0,2)，沿著方向 𝐚 = [2,0,1]，求方向導數。｜中華大學土木系呂志宗特聘教授 скачать в хорошем качестве

【詳細解題動畫】提要227：已知 f = 1/√(x² + y² + z²)，在 P: (1,0,2)，沿著方向 𝐚 = [2,0,1]，求方向導數。｜中華大學土木系呂志宗特聘教授

2026-03-12 🔴[Detailed Problem-solving Animation] Summary 227: Given 𝐚 = [2,0,1], f = 1/√(x² + y² + z²). Find the directional derivative 𝐷ᵤ𝑓 at (1,0,2) in the direction of 𝐚 with 𝐮 = 𝐚/|𝐚|.｜Instructor: John C.-C. Lu, Distinguished Professor, Department of Civil Engineering, Chung Hua University, Taiwan 🔴本題是 [2024年國立中山大學研究所入學考試試題]，今以動畫講解之，請參閱，謝謝！ ★ ★ The 2024 National Sun Yat-sen University Graduate School Entrance Exam Questions. It is explained in an animation. Please take a moment to browse through it. Thank you! ★ ① 第1種解法：方向導數 𝐷ᵤ𝑓(𝑃) 為量測 𝑓(𝑥,𝑦,𝑧) 在點 𝑃(𝑥,𝑦,𝑧) 引致的最大增量方向於單位向量 𝐮 方向的投影量。The directional derivative 𝐷ᵤ𝑓(𝑃) measures the rate of change of 𝑓(𝑥,𝑦,𝑧) as (𝑥,𝑦,𝑧) varies from 𝑃 in the direction of the unit vector 𝐮. ★ ② 符號運算軟體講解：https://x.chu.edu.tw/294MKH/ Online Tool for Symbolic Calculation: https://x.chu.edu.tw/294MKH/ [動畫問卷｜Animations Questionnaire] https://forms.gle/YjbcN4SZsBGqURxv6 🔴【運用 SUNO AI 編輯動畫音樂】 [SUNO AI Prompt] Cabaret, 1920s, jazz influence, piano-driven