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Ex 5.4, 3 - 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, 3 Differentiate 𝑤.𝑟.𝑡. 𝑥 in, 〖 𝑒〗^(𝑥^3 ) Let 𝑦 =〖 𝑒〗^(𝑥^3 ) " " Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑(𝑦)/𝑑𝑥 = 𝑑(〖 𝑒〗^(𝑥^3 ) )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 〖 𝑒〗^(𝑥^3 ) . 𝑑(𝑥^3 )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 〖 𝑒〗^(𝑥^3 ) . 3𝑥^2 𝒅𝒚/𝒅𝒙 = 𝟑𝒙^𝟐 〖 𝒆〗^(𝒙^𝟑 )
