# Misc 16 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 16 If cos𝑦=𝑥 cos(𝑎 + 𝑦), with cos𝑎 ≠ ± 1, prove that 𝑑𝑦𝑑𝑥 = 𝑐𝑜𝑠2(𝑎 + 𝑦) sin𝑎 Given cos𝑦 = 𝑥 cos(𝑎 + 𝑦) cos𝑦cos(𝑎 + 𝑦) = 𝑥 𝑥 = cos𝑦cos(𝑎 + 𝑦) Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑 𝑥𝑑𝑥 = 𝑑𝑑𝑥 cos𝑦 cos 𝑎 + 𝑦 1 = 𝑑𝑑𝑥 cos𝑦 cos 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑦 1 = 𝑑𝑑𝑦 cos𝑦 cos 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 1 = 𝑑 cos𝑦𝑑𝑦 . cos 𝑎 + 𝑦 − 𝑑 cos 𝑎 + 𝑦𝑑𝑦 . cos𝑦 cos 𝑎 + 𝑦2 . 𝑑𝑦𝑑𝑥 1 = − sin𝑦 . cos 𝑎 + 𝑦 − −sin 𝑎 + 𝑦 𝑑 𝑎 + 𝑦𝑑𝑦 . cos𝑦 cos2 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 1 = − sin𝑦 . cos 𝑎 + 𝑦 + sin 𝑎 + 𝑦 0 + 1 . cos𝑦 cos2 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 1 = sin 𝑎 + 𝑦 . cos𝑦 − cos 𝑎 + 𝑦 . sin𝑦 cos2 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 1 = sin 𝑎 + 𝑦 − 𝑦 cos2 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 1 = sin 𝑎 + 𝑦 − 𝑦 cos2 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 1 = sin 𝑎 cos2 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 1 = sin 𝑎 + 𝑦 − 𝑦 cos2 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 1 = sin 𝑎 cos2 𝑎 + 𝑦 . 𝑑𝑦𝑑𝑥 cos2 𝑎 + 𝑦 sin 𝑎 = 𝑑𝑦𝑑𝑥 𝒅𝒚𝒅𝒙 = 𝒄𝒐𝒔𝟐 𝒂 + 𝒚 𝒔𝒊𝒏 𝒂

Finding derivative of Implicit functions

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.