Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Last updated at Jan. 16, 2020 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Transcript

Find the derivative of f given by f (x) = sec–1 𝑥 assuming it exists. Let 𝑦 = sec^(–1) 𝑥 𝑠𝑒𝑐𝑦= 𝑥 𝑥 =𝑠𝑒𝑐𝑦 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑥/𝑑𝑥 = (𝑑 (𝑠𝑒𝑐𝑦 ))/𝑑𝑥 1 = (𝑑 (𝑠𝑒𝑐𝑦 ))/𝑑𝑥 We need 𝑑𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (sec𝑦 ))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦 1 = tan𝑦 .sec𝑦 . 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥 tan𝑦 .sec𝑦= 1 𝑑𝑦/𝑑𝑥 = 1/(𝒕𝒂𝒏𝒚 .〖 sec〗𝑦 ) 𝑑𝑦/𝑑𝑥 = 1/((√(〖𝐬𝐞𝐜〗^𝟐𝒚 − 𝟏)) .〖 sec〗𝑦 ) Putting value of 𝑠𝑒𝑐𝑦 = 𝑥 𝑑𝑦/𝑑𝑥 = 1/((√(𝑥^2 − 1 ) ) . 𝑥) 𝑑𝑦/𝑑𝑥 = 1/(𝑥 √(𝑥^2 − 1 ) ) As 𝑦 = sec^(−1) 𝑥 So, 𝑠𝑒𝑐𝑦 = 𝑥 Hence 𝒅(〖𝒔𝒆𝒄〗^(–𝟏) 𝒙)/𝒅𝒙 = 𝟏/(𝒙 √(𝒙^𝟐 − 𝟏 ) ) As tan2 θ = sec2 θ – 1, tan θ = √("sec2 θ – 1" )

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) You are here

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

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

About the Author

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.