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Ex 5.4, 7 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 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, 7 Differentiate w.r.t. x in, √(𝑒^√𝑥 ), x > 0Let 𝑦 = √(𝑒^√𝑥 ) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑦^′ = (√(𝑒^√𝑥 ))^′ 𝑦^′ = 1/(2 √(𝑒^√𝑥 )) × (𝑒^√𝑥 )^′ 𝑦^′ = 1/(2 √(𝑒^√𝑥 )) × 𝑒^√𝑥 . × (√𝑥)^′ 𝑦^′ = 1/(2 √(𝑒^√𝑥 )) × 𝑒^√𝑥 . × 1/(2√𝑥) 𝑦^′ = 𝑒^√𝑥/(4√𝑥 . √(𝑒^√𝑥 )) 𝑦^′ = 𝒆^√𝒙/(𝟒√(𝒙 . 𝒆^√𝒙 ))
