Class 12 Maths Ex 5.3 Q13 | Derivative of cos⁻¹(2x/(1+x²)) | Step-by-Step NCERT Solution
Learn how to find dy/dx for y = cos⁻¹(2x/(1+x²)) using substitution and trigonometric identities. This is a critical inverse trigonometric differentiation problem from NCERT Class 12 Chapter 5 (Continuity and Differentiability), Exercise 5.3, Question 13.
📚 What You’ll Learn:
✅ How to use substitution (x = tan θ) to simplify inverse functions
✅ Apply trigonometric identities: sin(2θ) and cos(π/2 – θ) equivalence
✅ Convert inverse trig expressions to simpler forms before differentiating
✅ Find the final derivative: dy/dx = -2/(1+x²)
⏱️ Video Timestamps:
0:00 — Introduction & Problem Statement
0:17 — Substitution Method (x = tan θ)
0:43 — Trigonometric Identity: 2tan(θ)/(1+tan²(θ)) = sin(2θ)
1:13 — Converting sin(2θ) to cos(π/2 – 2θ)
1:40 — Simplifying to y = π/2 – 2tan⁻¹(x)
2:00 — Differentiation & Final Answer: dy/dx = -2/(1+x²)
📖 Curriculum Reference:
NCERT Class 12 Maths
Chapter 5: Continuity and Differentiability
Exercise 5.3, Question 13
Covers: Derivatives of inverse trigonometric functions, substitution methods, trigonometric identities
💡 This problem is commonly asked in:
✔ CBSE Board Exams (Class 12 Mathematics)
✔ Monthly/Term Tests
✔ Competitive Exam Practice (JEE Main/Advanced)
✔ Engineering Entrance Preparations
🎯 Next Question: Watch our next video for Ex 5.3 Q14 and continue mastering inverse trigonometric differentiation
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