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Ex 5.3, 1 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Oct. 28, 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, 1 Find ππ¦/ππ₯ in, 2π₯ + 3π¦ = sinβ‘π₯ Given 2π₯+3π¦ = sinβ‘π₯ Differentiating both sides π€.π.π‘.π₯ (π (2π₯ + 3π¦))/(ππ₯ ) = (π(sinβ‘γπ₯)γ)/(ππ₯ ) (π(2π₯))/(ππ₯ ) +(π(3π¦))/(ππ₯ )=(π(sinβ‘γπ₯)γ)/(ππ₯ ) 2 (π(π₯))/(ππ₯ ) +"3" (π(π¦))/(ππ₯ )=(π(sinβ‘γπ₯)γ)/(ππ₯ ) 2 + 3 ππ¦/(ππ₯ ) = πππβ‘π 3 ππ¦/(ππ₯ ) = cosβ‘π₯ β 2 π π/(π π ) = π/π (πππβ‘π β 2)
