# Ex 5.3, 15 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Jan. 3, 2020 by Teachoo

Last updated at Jan. 3, 2020 by Teachoo

Transcript

Ex 5.3, 15 Find ๐๐ฆ/๐๐ฅ in, y = secโ1 (1/( 2๐ฅ2โ1 )), 0 < x < 1/โ2 y = secโ1 (1/( 2๐ฅ^2 โ 1 )) ๐๐๐โก๐ = 1/(2๐ฅ^2 โ 1) ๐/๐๐จ๐ฌโก๐ = 1/(2๐ฅ^2 โ 1) cosโก๐ฆ = 2๐ฅ2โ1 y = cos โ1 (2๐ฅ2โ1) Putting ๐ฅ = cosโกฮธ ๐ฆ = cos โ1 (2๐๐๐ 2๐โ1) ๐ฆ = cos โ1 (cosโก2 ๐) ๐ฆ = 2๐ Putting value of ฮธ = cosโ1 x ๐ฆ = 2 ใ๐๐๐ ใ^(โ1) ๐ฅ Differentiating both sides ๐ค.๐.๐ก.๐ฅ . (๐(๐ฆ))/๐๐ฅ = (๐ (2ใ๐๐๐ ใ^(โ1) ๐ฅ" " ))/๐๐ฅ ๐๐ฆ/๐๐ฅ = 2 (๐ (ใ๐๐๐ ใ^(โ1) ๐ฅ" " ))/๐๐ฅ ๐๐ฆ/๐๐ฅ = 2 . ((โ1)/โ(1 โ ๐ฅ^2 )) ๐ ๐/๐ ๐ = (โ๐)/โ(๐ โ ๐^๐ ) (๐๐๐ โก2๐ " = 2 " ใ๐๐๐ ใ^2 ๐โ1) ((ใ๐๐๐ ใ^(โ1) ๐ฅ")โ = " (โ1)/โ(1 โ ๐ฅ^2 ))

Finding derivative of Inverse trigonometric functions

Derivative of cos-1 x (Cos inverse x)

Example 26 Important

Example 27

Derivative of cot-1 x (cot inverse x)

Derivative of sec-1 x (Sec inverse x)

Derivative of cosec-1 x (Cosec inverse x)

Ex 5.3, 14

Ex 5.3, 9 Important

Ex 5.3, 13 Important

Ex 5.3, 12 Important

Ex 5.3, 11 Important

Ex 5.3, 10 Important

Ex 5.3, 15 Important You are here

Misc 5 Important

Misc 4

Misc 13 Important

Chapter 5 Class 12 Continuity and Differentiability

Concept wise

- Checking continuity at a given point
- Checking continuity at any point
- Checking continuity using LHL and RHL
- Algebra of continous functions
- Continuity of composite functions
- Checking if funciton is differentiable
- Finding derivative of a function by chain rule
- Finding derivative of Implicit functions
- Finding derivative of Inverse trigonometric functions
- Finding derivative of Exponential & logarithm functions
- Logarithmic Differentiation - Type 1
- Logarithmic Differentiation - Type 2
- Derivatives in parametric form
- Finding second order derivatives - Normal form
- Finding second order derivatives- Implicit form
- Proofs
- Verify Rolles theorem
- Verify Mean Value Theorem

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.