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Ex 5.7, 1 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at August 11, 2026 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
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Transcript
Ex 5.7, 1 Find the second order derivatives of the function ๐ฅ^2 + 3๐ฅ + 2 Let ๐ฆ = ๐ฅ^2 + 3๐ฅ + 2 Differentiating ๐ค.๐.๐ก.๐ฅ ๐๐ฆ/๐๐ฅ = (๐(๐ฅ^2 + 3๐ฅ + 2))/(๐๐ฅ ) ๐๐ฆ/๐๐ฅ = (๐(๐ฅ^2))/๐๐ฅ + (๐(3๐ฅ) )/๐๐ฅ + (๐(2) )/๐๐ฅ ๐๐ฆ/๐๐ฅ = 2๐ฅ+3+0 ๐ ๐/๐ ๐ = ๐๐ + ๐ Again Differentiating ๐ค.๐.๐ก.๐ฅ ๐ /๐ ๐ (๐ ๐/๐ ๐) = (๐ (๐๐ + ๐))/๐ ๐ (๐^2 ๐ฆ)/ใ๐๐ฅใ^2 = ๐(2๐ฅ)/๐๐ฅ + ๐(3)/๐๐ฅ (๐^2 ๐ฆ)/ใ๐๐ฅใ^2 = 2 + 0 (๐ ^๐ ๐)/ใ๐ ๐ใ^๐ = 2
