Ex 5.3, 11 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Finding derivative of Inverse trigonometric functions
Derivative of cos-1 x (Cos inverse x)
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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
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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, 11 Find ππ¦/ππ₯ in, π¦ = cosβ1 ((1β π₯^2)/( 1+ π₯2 )) , 0 < x < 1 π¦ = cosβ1 ((1β π₯^2)/( 1+ π₯2 )) Putting x = tan ΞΈ y = γπππ γ^(β1) ((1βtanβ‘2 π)/(1+ tanβ‘2 π)) y = cosβ1 (cos 2π) π¦ =2ΞΈ Putting value of ΞΈ = γπ‘ππγ^(β1) π₯ π¦=2 (γπ‘ππγ^(β1) π₯) (cosβ‘2ΞΈ " =" (1 β tanβ‘2 π)/(1+ tanβ‘2 π)) Since x = tan ΞΈ β΄ γπ‘ππγ^(β1) x = ΞΈ
