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Ex 5.4, 5 - 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, 5 Differentiate w.r.t. x in , 〖log 〗(cos〖𝑒^𝑥 〗 )Let 𝑦 = 〖log 〗(cos〖𝑒^𝑥 〗 ) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑(𝑦)/𝑑𝑥 = 𝑑(〖log 〗(cos〖𝑒^𝑥 〗 ) )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/cos〖𝑒^𝑥 〗 . 𝑑(cos〖𝑒^𝑥 〗 )/𝑑𝑥 = 1/cos〖𝑒^𝑥 〗 . (−sin〖𝑒^𝑥 〗 ) . 𝑑(𝑒^𝑥 )/𝑑𝑥 = 1/cos〖𝑒^𝑥 〗 . (−sin〖𝑒^𝑥 〗 ) . 𝑒^𝑥 = (−sin〖𝑒^𝑥 〗)/cos〖𝑒^𝑥 〗 . 𝑒^𝑥 = −tan〖𝑒^𝑥 〗 . 𝑒^𝑥 = −𝒆^𝒙 . 𝒕𝒂𝒏〖𝒆^𝒙 〗 (𝐴𝑠 𝑑/𝑑𝑥 (𝑙𝑜𝑔𝑥 )= 1/𝑥) (𝐴𝑠 𝑑/𝑑𝑦 (cos𝑥 )=〖−sin〗𝑥 )
