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Ex 5.4, 7 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at August 17, 2026 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, 7 Differentiate w.r.t. x in, โ(๐^โ๐ฅ ), x > 0Let ๐ฆ = โ(๐^โ๐ฅ ) Differentiating both sides ๐ค.๐.๐ก.๐ฅ ๐ฆ^โฒ = (โ(๐^โ๐ฅ ))^โฒ ๐ฆ^โฒ = 1/(2 โ(๐^โ๐ฅ )) ร (๐^โ๐ฅ )^โฒ ๐ฆ^โฒ = 1/(2 โ(๐^โ๐ฅ )) ร ๐^โ๐ฅ . ร (โ๐ฅ)^โฒ ๐ฆ^โฒ = 1/(2 โ(๐^โ๐ฅ )) ร ๐^โ๐ฅ . ร 1/(2โ๐ฅ) ๐ฆ^โฒ = ๐^โ๐ฅ/(4โ๐ฅ . โ(๐^โ๐ฅ )) ๐ฆ^โฒ = ๐^โ๐/(๐โ(๐ . ๐^โ๐ ))
