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Example 23 - 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
Example 23 Find ππ¦/ππ₯ , if y + sin y = cosβ‘π₯ y + sin y = cos x Differentiating both sides by x ππ¦/ππ₯ + (π(sinβ‘γπ¦)γ)/ππ₯ = (π (ππ¨π¬β‘γπ)γ)/π π ππ¦/ππ₯ + (π(γsin γβ‘γπ¦)γ)/ππ₯ = β sin x ππ¦/ππ₯ + (π (π¬π’π§β‘γπ)γ)/π π . ππ¦/ππ₯ = β sin x ππ¦/ππ₯ + cos y ππ¦/ππ₯ = β sin x ππ¦/ππ₯ (1 + cos y) = β sin x π π/π π = (βπππβ‘π)/((π + πππβ‘γπ)γ )
