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Ex 5.4, 8 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Finding derivative of Exponential & logarithm functions
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
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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
Transcript
Ex 5.4, 8 Differentiate w.r.t. x in, log(log𝑥), x > 1Let 𝑦 = log (log𝑥) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑(𝑦)/𝑑𝑥 = (𝑑(log (log𝑥)) )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/log𝑥 × 𝑑(log𝑥)/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/log𝑥 × 1/𝑥 𝒅𝒚/𝒅𝒙 = 𝟏/(𝒙 𝒍𝒐𝒈𝒙 ) (𝐴𝑠 𝑑/𝑑𝑥 (𝑙𝑜𝑔𝑥 )= 1/𝑥) (𝐴𝑠 𝑑/𝑑𝑥 (𝑙𝑜𝑔𝑥 )= 1/𝑥)
