# Ex 5.3, 10

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 5.3, 10 Find 𝑑𝑦𝑑𝑥 in, 𝑦 = tan–1 3𝑥− 𝑥3 1− 3𝑥2 , − 1 3 < 𝑥 < 1 3 𝑦 = tan–1 3𝑥− 𝑥3 1− 3𝑥2 Putting x = tan θ y = 𝑡𝑎𝑛−1 3 tan𝜃 − tan3𝜃1 − 3 tan2 𝜃 y = 𝑡𝑎𝑛−1 ( tan3 𝜃) 𝑦 = 3𝜃 Putting value of θ = 𝑡𝑎𝑛−1 𝑥 𝑦 = 3 (𝑡𝑎𝑛−1 𝑥) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 . 𝑑(𝑦)𝑑𝑥 = 𝑑 3 (𝑡𝑎𝑛−1 𝑥) 𝑑𝑥 𝑑𝑦𝑑𝑥 =3 𝑑 (𝑡𝑎𝑛−1 𝑥) 𝑑𝑥 𝑑𝑦𝑑𝑥 = 3 11 + 𝑥2 𝒅𝒚𝒅𝒙 = 𝟑𝟏 + 𝒙𝟐

Ex 5.1, 9
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Ex 5.1, 13 Important

Ex 5.1, 16 Important

Ex 5.1, 18 Important

Ex 5.1, 28 Important

Ex 5.1, 30 Important

Ex 5.1, 34 Important

Ex 5.2, 5 Important

Ex 5.2, 9 Important

Ex 5.2, 10 Important

Ex 5.3, 10 Important You are here

Ex 5.3, 14 Important

Example 32 Important

Example 33 Important

Ex 5.5,6 Important

Ex 5.5, 7 Important

Ex 5.5, 11 Important

Ex 5.5, 16 Important

Ex 5.6, 7 Important

Ex 5.6, 11 Important

Example 41 Important

Ex 5.7, 14 Important

Example 42 Important

Ex 5.8, 5 Important

Example 44 Important

Example 45 Important

Example 47 Important

Misc 6 Important

Misc 15 Important

Misc 16 Important

Misc 23 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.