【公式導出シリーズ】三角関数の微分公式の証明
⭐️ "Oshie Math" allows you to ask Hayashi unlimited questions for a fixed monthly fee. You can try asking questions for free once! https://oshiemath.com/ ⭐️ "Hayashi Math Class," a specialized mathematics school where you can receive direct instruction from Hayashi. Please come for a trial lesson and interview! https://hayashi-math.com/ ✅ Official LINE for students applying to top universities: https://lin.ee/lI7n1SJ Subscriber benefits & live streams for applicants ℹ️ Shunsuke Hayashi's profile https://hayashishunsuke.com/profile/ ・Graduated from Sakae Higashi Junior High School → Chikuma High School → University of Tokyo, Faculty of Science, Department of Physics ・Scored 90% on the second-stage mathematics exam at the University of Tokyo, passing the exam as a current student ・2014 Japan Physics Olympiad Gold Medal ・Placed first place in the 2014 University of Tokyo Physics Mock Exam ℹ️ Please note ・The explanations are Shunsuke Hayashi's own and are not official university information. ・Amazon Associates links will be used when introducing books, etc. This time, we'll be deriving the derivative formula for trigonometric functions, which appears in High School Mathematics III. This is not to be underestimated, as some questions have actually appeared on university entrance exams. Write down the derivative according to the definition, expand it using the addition theorem... It's really just a straightforward calculation, but I think many people have trouble with it. Please watch this video to master it!

【公式導出シリーズ】指数関数の微分公式
![[Formula Derivation Series] Proof of the Differentiation Formula for Logarithmic Functions](https://i.ytimg.com/vi/pvsPmW6MUXs/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLBRgJgc64AKXpoMdVGww3KNp_do3Q)
[Formula Derivation Series] Proof of the Differentiation Formula for Logarithmic Functions
![Proof of the actual question “The derivative of sinx is cosx” [Osaka University].](https://i.ytimg.com/vi/jpqkGIkcAvM/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLCxaCsAbcv1XaeU_JNF6RsFxxlSfw)
Proof of the actual question “The derivative of sinx is cosx” [Osaka University].

A lesson on the cosine theorem that you'll never forget

数Ⅲ微分計算#13/26【三角関数の微分(証明編)】sin x/xの極限計算で証明!|入試基礎
![[Slow explanation] The true nature of "sin, cos, tan" - the nemesis of liberal arts students](https://i.ytimg.com/vi/p55eSlC-Uf8/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLCbcQs4GnOx4ka0ZrCRr8923HxhZA)
[Slow explanation] The true nature of "sin, cos, tan" - the nemesis of liberal arts students

【公式導出シリーズ】積の微分の公式を導こう

I want all trig functions in one integral!

If you don't feel like going to school, then watch this video – my tips for better grades.

Who is Smarter? Engineer vs Chinese 5th Grader
![[Background] An easy way to shift the contents of trigonometric functions.](https://i.ytimg.com/vi/WsqtlQqtQ3A/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLB6xUbHTu2Jl79uAzWzy6zyfbSy8Q)
[Background] An easy way to shift the contents of trigonometric functions.

Why the derivative of the area of a circle is the circumference of the circle

【公式導出シリーズ】点と直線の距離の公式

【高校数学】数Ⅲ-96 三角関数の導関数①

Thinking process when solving integrals

Die Zombie-Simulation, die niemand erklären kann

もう一つの虚数単位「j」
![A detour to rigorously prove the addition theorem! [This week's theorem/formula No. 2]](https://i.ytimg.com/vi/hPF158zkFD8/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLD1qyTyW-cgl2JnyWCVptJDTfc_Cw)
A detour to rigorously prove the addition theorem! [This week's theorem/formula No. 2]

I visited the world's hardest math class

