Class #7 📘 Differentiation | Exercise 1.1 Question 3

Welcome back to our **12th State Board Mathematics Series**\! In today's session, we continue our deep dive into **Differentiation**, specifically focusing on Exercise 1.1, Question 3. In this video, we cover several important sub-questions, including a detailed look at Question 15 (which was previously skipped) and subsequent problems like 17, 18, and 19. This lecture is packed with essential logarithmic properties and trigonometric identities that are crucial for scoring high in your Board exams. *Key Concepts Covered:* *Trigonometric Simplification:* Using $1 \pm \sin(x)$ formulas and $1 \pm \cos(x)$ identities to simplify functions before differentiating. *Logarithmic Rules:* Mastering $\log(a/b)$, $\log(a \cdot b)$, and $\log(a^b)$ to break down complex expressions. *The Chain Rule:* Step-by-step application of the Chain Rule to ensure accuracy in multi-layered functions. *Special Substitutions:* Using $\tan(\pi/4)$ for simplification and understanding the relationship between $e^{\log(x)}$ and other base-specific log properties. *Timestamps:* *00:00* – Introduction & Recap of Question 3 *00:30* – Solving Question 15: Handling $\sin$ functions and trigonometric identities *05:30* – Simplification using $\tan(\pi/4)$ adjustment *09:12* – Differentiation of simplified logarithmic functions *14:28* – Solving Question 17: Log properties ($\log(a/b)$ and $\log(a \cdot b)$) *20:06* – Solving Question 18: Constant terms and $\log(a)$ properties *24:52* – Solving Question 19: Advanced log base properties and trigonometric identities *30:16* – Solving Question 20: Applying the Quotient Rule ($u/v$ rule) & Homework Task *Resources:* Make sure to have your *Formula Copy* ready and mark the steps highlighted with a *\#* or \*\*\*\*\* for important adjustments\! If you missed the previous session where we covered earlier sub-questions, catch up here: [Previous Video Title](https://studio.youtube.com/video/sm9R...) (Note: Ensure you link the actual previous video here). *Don't forget to:* ✅ *Like* if this explanation helped you clear your concepts. ✅ *Subscribe* for more 12th Board prep content. ✅ *Comment* below if you have any doubts or questions regarding the homework problem\! \#Differentiation \#12thBoards \#HSCMaths \#Calculus \#ScholarTude \#MathsTutorial \#StateBoardSeries