Exercise 5.7 | Class 12 Maths | Second Order Derivative | Continuity & Differentiability

📘 Class 12 Chapter 5 – Continuity and Differentiability | SECOND ORDER DERIVATIVE | Complete Exercise 5.7 Solutions
In this video, Faiz Sir (Infinix Classes) explains Second Order Derivative in the most simple and exam-oriented way.
Is video me humne NCERT Class 12 Maths Exercise 5.7 ke sare questions solve kiye hain, jisme advanced differentiation concepts use hote hain.

👉 Class 12 CBSE, Boards, JEE (Basics), CUET aur school exams ke liye bahut hi important chapter.
👉 Step-by-step derivation + formulas + shortcuts + tricks included.

📝 Topics Covered in This Video:
🔹 Second Order Derivative Concepts

– d²y/dx² basics
– Higher order differentiation
– Relations involving second derivative

🔹 Exercise 5.7 Questions Covered:

x³ log x

eˣ sin 5x

e⁶ˣ cos 3x

tan⁻¹ x

log(log x)

sin(log x)

🔹 Prove-Type Questions:

If y = 5cos x – 3sin x, prove that d²y/dx² + y = 0

If y = cos⁻¹ x, find d²y/dx² in terms of y

If y = 3cos(log x) + 4sin(log x), show that x²y² + xy¹ + y = 0

If y = A eᵐˣ + B eⁿˣ, show relation with second derivative

If y = 500e⁷ˣ + 600e⁻⁷ˣ, show that d²y/dx² = 49y

If eʸ(x + 1) = 1, show that d²y/dx² = (dy/dx)²

If y = (tan⁻¹ x)², show that (x² + 1)² y² + 2x(x² + 1) y¹ = 2

⭐ Why Watch This Video?

✔ 100% NCERT Based
✔ Board Exam Oriented Explanations
✔ Short Tricks & Logic Based Learning
✔ Notes + Concept Clarity
✔ Faiz Sir’s Trusted Teaching Style

📚 Suitable For:

✔ Class 12 CBSE Students
✔ Class 12 State Board Students
✔ JEE Aspirants (Basics)
✔ CUET Preparation
✔ Competitive Exams (Foundation)

🔔 Don’t Forget:

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