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Ex 5.6, 1 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at May 29, 2023 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
Transcript
Ex 5.6, 1 If x and y are connected parametrically by the equations without eliminating the parameter, Find ππ¦/ππ₯, x = 2γππ‘γ^2, y = γππ‘γ^4Here ππ¦/ππ₯ = (ππ¦/ππ‘)/(ππ₯/ππ‘) Calculating π π/π π π¦ = γππ‘γ^4 ππ¦/ππ‘ " =" γ4ππ‘γ^(4 β1) "=" γ4ππ‘γ^3 Calculating π π/π π π₯ = 2γππ‘γ^2 ππ₯/ππ‘ " =" 2 Γ 2ππ‘ "=" 4ππ‘ Now, ππ¦/ππ₯ = (ππ¦/ππ‘)/(ππ₯/ππ‘) Putting values ππ¦/ππ₯ = (4ππ‘^3)/4ππ‘ π π/π π = t2
