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

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.3, 5 Find ๐๐ฆ/๐๐ฅ in, ๐ฅ2 + ๐ฅ๐ฆ + ๐ฆ2 = 100 ๐ฅ2 + ๐ฅ๐ฆ + ๐ฆ2 = 100 Differentiating both sides ๐ค.๐.๐ก.๐ฅ . ๐(๐ฅ2 + ๐ฅ๐ฆ + ๐ฆ2)/๐๐ฅ = (๐ (100))/๐๐ฅ ๐(๐ฅ2)/๐๐ฅ + ๐(๐ฅ๐ฆ)/๐๐ฅ + (๐(๐ฆ2))/๐๐ฅ = (๐ (100))/๐๐ฅ 2๐ฅ^(2โ1) + (๐(๐ฅ๐ฆ))/๐๐ฅ + (๐(๐ฆ2))/๐๐ฅ ร ๐๐ฆ/๐๐ฆ = 0 2๐ฅ + (๐(๐ฅ๐ฆ))/๐๐ฅ + (๐(๐ฆ2))/๐๐ฆ ร ๐๐ฆ/๐๐ฅ = 0 2๐ฅ + (๐(๐ฅ๐ฆ))/๐๐ฅ + 2๐ฆ^(2โ1) . ๐๐ฆ/๐๐ฅ = 0 2๐ฅ + (๐(๐ฅ๐ฆ))/๐๐ฅ + 2๐ฆ . ๐๐ฆ/๐๐ฅ = 0 Using product rule in ๐ฅ๐ฆ = ๐ฅ^โฒ ๐ฆ+๐ฆ^โฒ ๐ฅ 2๐ฅ + ((๐(๐ฅ))/๐๐ฅ .๐ฆ+๐(๐ฆ)/๐๐ฅ.๐ฅ) + 2๐ฆ . ๐๐ฆ/๐๐ฅ = 0 2๐ฅ + (1 .๐ฆ+๐ฅ.๐(๐ฆ)/๐๐ฅ) + 2๐ฆ . ๐๐ฆ/๐๐ฅ = 0 2๐ฅ + ๐ฆ + ๐ฅ . ๐๐ฆ/๐๐ฅ + 2๐ฆ . ๐๐ฆ/๐๐ฅ = 0 (2๐ฅ + ๐ฆ) + ๐๐ฆ/๐๐ฅ . (๐ฅ + 2๐ฆ) = 0 ๐๐ฆ/๐๐ฅ . (๐ฅ + 2๐ฆ) = โ (2๐ฅ + ๐ฆ) ๐ ๐/๐ ๐ = (โ( ๐๐ + ๐ ))/( ( ๐ + ๐๐ ))

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.