# Ex 5.3, 7 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Sept. 17, 2019 by Teachoo

Last updated at Sept. 17, 2019 by Teachoo

Transcript

Ex 5.3, 7 Find 𝑑𝑦𝑑𝑥 in, sin2 𝑦 +cos 𝑥𝑦 =𝜋 sin2 𝑦 +cos 𝑥𝑦 =𝜋 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 . 𝑑 sin2 𝑦 + cos 𝑥𝑦𝑑𝑥 = 𝑑 𝜋𝑑𝑥 𝑑 (sin2 𝑦)𝑑𝑥 + 𝑑 ( cos 𝑥𝑦)𝑑𝑥= 0 Calculating Derivative of sin2 𝑦 & cos (x𝑦) separately Calculating Derivative of 𝒔𝒊𝒏𝟐 𝒚 𝑑 (sin2 𝑦)𝑑𝑥= 𝑑 (sin2 𝑦)𝑑𝑥 × 𝑑𝑦𝑑𝑦 = 𝑑 (sin2(𝑦))𝑑𝑥 × 𝑑𝑦𝑑𝑥 =2 𝑠𝑖𝑛2−1 𝑥. 𝑑( sin𝑦)𝑑𝑦 × 𝑑𝑦𝑑𝑥 = 2 sin𝑦 . cos𝑦 × 𝑑𝑦𝑑𝑥 Calculating Derivative of 𝒄𝒐𝒔 (𝒙𝒚) 𝑑( cos(𝑥𝑦))𝑑𝑥= − sin(𝑥𝑦) × 𝑑𝑑𝑥(𝑥𝑦) = − sin 𝑥𝑦× 𝑑 𝑥𝑑𝑥.𝑦+ 𝑑 𝑦𝑑𝑥.𝑥 = − sin 𝑥𝑦 . 1.𝑦+𝑥 𝑑𝑦𝑑𝑥 = − sin 𝑥𝑦 𝑦+𝑥 𝑑𝑦𝑑𝑥 = − sin 𝑥𝑦 . 𝑦− sin 𝑥𝑦 . 𝑥 𝑑𝑦𝑑𝑥 = −𝑦 sin 𝑥𝑦 − sin 𝑥𝑦 . 𝑥 𝑑𝑦𝑑𝑥 Now, 𝑑 (𝑠𝑖𝑛2𝑦)𝑑𝑥+ 𝑑 ( cos(𝑥𝑦)) 𝑑𝑥 = 0 Putting values 2 sin𝑦. cos𝑦 . 𝑑𝑦𝑑𝑥 + − 𝑦 sin 𝑥𝑦−𝑥 sin 𝑥𝑦 𝑑𝑦𝑑𝑥 = 0 2 sin𝑦. cos𝑦 . 𝑑𝑦𝑑𝑥 − 𝑦 sin(𝑥𝑦) − 𝑥 sin(𝑥𝑦) 𝑑𝑦𝑑𝑥 = 0 2 sin𝑦 cos𝑦 𝑑𝑦𝑑𝑥 −𝑥 sin(𝑥𝑦) 𝑑𝑦𝑑𝑥 = 𝑦 sin(𝑥𝑦) 𝑑𝑦𝑑𝑥 (2 sin𝑦 cos𝑦 − 𝑥 sin(𝑥𝑦) = 𝑦 sin(𝑥𝑦) 𝑑𝑦𝑑𝑥 = 𝑦 sin(𝑥𝑦)2 sin 𝑦 cos𝑦 − 𝑥 sin𝑥𝑦 𝒅𝒚𝒅𝒙 = 𝒚 𝒔𝒊𝒏(𝒙𝒚) 𝒔𝒊𝒏 𝟐𝒚− 𝒙 𝒔𝒊𝒏𝒙𝒚

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.