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Example 31 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Derivatives in parametric form
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
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Transcript
Example 31 Find ππ¦/ππ₯ , if π₯ = π cosβ‘π, π¦ = π sin ΞΈ.Here ππ¦/ππ₯ = (ππ¦/ππ)/(ππ₯/ππ) Calculating π π/π π½ π¦ = π sin ΞΈ ππ¦/ππ = π(π sin π)/ππ ππ¦/ππ = π πππβ‘π½ Calculating π π/π π½ π¦ = π cos ΞΈ ππ¦/ππ = π(π cos π)/ππ ππ¦/ππ = βπ πππβ‘π½ Now, ππ¦/ππ₯ = (ππ¦/ππ)/(ππ₯/ππ) ππ¦/ππ₯ = (π cosβ‘ΞΈ)/(βπ sinβ‘ΞΈ ) π π/π π = βππ¨πβ‘π
