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Example 26 (i) - Chapter 5 Class 12 Continuity and Differentiability
Last updated at December 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
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Transcript
Example 26 Differentiate the following w.r.t. x: (i) 𝑒^(–𝑥)Let 𝑦 = 𝑒^(–𝑥) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑𝑦/𝑑𝑥 = 𝑑(𝑒^(−𝑥) )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 𝑒^(−𝑥) . 𝑑(−𝑥)/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 𝑒^(−𝑥) (−1) . 𝒅𝒚/𝒅𝒙 = 〖−𝒆〗^(−𝒙)
