# Ex 5.7, 11 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 5.7, 11 If y=5 cos𝑥−3 sin𝑥 ,prove that 𝑑2𝑦𝑑𝑥2 + y = 0 First calculating 𝒅𝟐𝒚𝒅𝒙𝟐 y = 5 cos𝑥−3 sin𝑥 Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑦𝑑𝑥 = 𝑑(5 cos𝑥−3 sin𝑥)𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑑(5 cos𝑥)𝑑𝑥 − 𝑑(3 sin𝑥)𝑑𝑥 𝑑𝑦𝑑𝑥 = 5 𝑑( cos𝑥)𝑑𝑥 − 3 𝑑( sin𝑥)𝑑𝑥 𝑑𝑦𝑑𝑥 = − 5 sin𝑥 − 3 cos𝑥 Again Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑑 (− 5 sin𝑥 − 3cos𝑥)𝑑𝑥 𝑑2𝑦𝑑 𝑥2 = 𝑑(5 sin𝑥)𝑑𝑥 − 𝑑(−3 cos𝑥)𝑑𝑥 𝑑2𝑦𝑑 𝑥2 = − 5 cos𝑥 − 3 (−sin𝑥) 𝑑2𝑦𝑑 𝑥2 = − 5 cos𝑥 + 3 sin𝑥 We need to prove 𝑑2𝑦𝑑 𝑥2 + y = 0 Solving LHS 𝑑2𝑦𝑑 𝑥2 + 𝑦 Putting values = (− 5 cos𝑥 + 3 sin𝑥) + ( 5 cos𝑥 − 3 sin𝑥) = − 5 cos𝑥 + 5 cos𝑥 + 3 sin𝑥 − 3 sin𝑥 = 0 Hence proved .

Finding second order derivatives- Implicit form

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.