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Ex 5.7, 2 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Finding second order derivatives - Normal 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
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Finding second order derivatives - Normal form
- Finding second order derivatives- Implicit form
- Proofs
- Verify Rolles theorem
- Verify Mean Value Theorem
Transcript
Ex 5.7, 2 Find the second order derivatives of the function 𝑥^20 Let y = 𝑥^20 Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑦/𝑑𝑥 = (𝑑(𝑥^20))/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 〖20𝑥〗^(20−1) 𝑑𝑦/𝑑𝑥 = 〖20𝑥〗^19 Again Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑/𝑑𝑥 (𝑑𝑦/𝑑𝑥) = (𝑑 (〖20𝑥〗^19))/𝑑𝑥 (𝑑^2 𝑦)/(𝑑𝑥^2 ) = (20 𝑑(𝑥^19))/𝑑𝑥 (𝑑^2 𝑦)/(𝑑𝑥^2 ) = 20 × 19 𝑥^(19−1) (𝑑^2 𝑦)/(𝑑𝑥^2 ) = 20 × 19 𝑥^18 (𝑑^2 𝑦)/(𝑑𝑥^2 ) = 380 𝑥^18 Thus, (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 ) = 380 𝒙^𝟏𝟖
