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Example 25 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at June 2, 2023 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
Example 25 Is it true that x = 𝑒 log𝑥 for all real x? x = e log x For x = 0 0 = elog 0 But log 0 is not defined. Hence, the equation is not defined for x = 0 For x < 0 x = e log x But log x is not defined for negative numbers Hence, equation is not defined for x < 0 For x > 0 x = e log x This is defined Hence, equation is defined for x > 0 Therefore, x = e log x is true for all positive values if x i.e. x > 0
