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Ex 5.3, 2 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
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
- 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 5.3, 2 Find ππ¦/ππ₯ in , 2π₯ + 3π¦ = sinβ‘π¦ . 2π₯ + 3π¦ = sinβ‘π¦ Differentiating both sides π€.π.π‘.π₯ π(2π₯ + 3π¦)/ππ₯ = (π (sinβ‘π¦ ))/ππ₯ π(2π₯)/ππ₯ +π(3π¦)/ππ₯= (π (sinβ‘π¦ ))/ππ₯ 2 ππ₯/ππ₯ +3π(π¦)/ππ₯= (π (sinβ‘π¦ ))/ππ¦ Γ ππ¦/ππ₯ 2 + 3 ππ¦/ππ₯ = cosβ‘π¦ "Γ " ππ¦/ππ₯ cosβ‘π¦ "Γ " ππ¦/ππ₯ β 3 ππ¦/ππ₯ = 2 (Derivative of π ππβ‘π₯ is πππ β‘π₯) ππ¦/ππ₯ (cos y β 3) = 2 π π/π π = π/((πππβ‘γπβπ)γ )
