# Ex 5.3, 13 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Jan. 3, 2020 by Teachoo

Last updated at Jan. 3, 2020 by Teachoo

Transcript

Ex 5.3, 13 Find ππ¦/ππ₯ in, y = cosβ1 (2π₯/( 1+ π₯2 )) , β1 < x < 1 π¦ = cosβ1 (2π₯/( 1+ π₯2 )) Let π₯ = tanβ‘π π¦ = cosβ1 ((2 tanβ‘π)/( 1 + π‘ππ2π )) π¦ = cosβ1 (sin 2ΞΈ) π¦ ="cosβ1" (γcos γβ‘(π/2 β2π) ) π¦ = π/2 β 2π Putting value of ΞΈ = tanβ1 x π¦ = π/2 β 2 γπ‘ππγ^(β1) π₯ Since x = tan ΞΈ β΄ γπ‘ππγ^(β1) x = ΞΈ Differentiating both sides π€.π.π‘.π₯ (π(π¦))/ππ₯ = (π (" " π/2 " β " γ2π‘ππγ^(β1) π₯" " ))/ππ₯ ππ¦/ππ₯ = 0 β 2 (πγ (π‘ππγ^(β1) π₯))/ππ₯ ππ¦/ππ₯ = β 2 (πγ (π‘ππγ^(β1) π₯))/ππ₯ ππ¦/ππ₯ = β 2 (1/(1 + π₯^2 )) π π/π π = (βπ)/(π + π^π ) ((γπ‘ππγ^(β1) π₯") β = " 1/(1 + π₯^2 ))

Finding derivative of Inverse trigonometric functions

Derivative of cos-1 x (Cos inverse x)

Example 26 Important

Example 27

Derivative of cot-1 x (cot inverse x)

Derivative of sec-1 x (Sec inverse x)

Derivative of cosec-1 x (Cosec inverse x)

Ex 5.3, 14

Ex 5.3, 9 Important

Ex 5.3, 13 Important You are here

Ex 5.3, 12 Important

Ex 5.3, 11 Important

Ex 5.3, 10 Important

Ex 5.3, 15 Important

Misc 5 Important

Misc 4

Misc 13 Important

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.