Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Last updated at Jan. 3, 2020 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Transcript

Misc 13 Find ππ¦/ππ₯ , if π¦=γπ ππγ^(βπ) π₯+γπ ππγ^(β1) β(1βπ₯2), β 1 β€ π₯ β€ 1 π¦=γπ ππγ^(βπ) π₯+γπ ππγ^(β1) β(1βπ₯^2 ) , β 1 β€ π₯ β€ 1 Put π₯ = π ππβ‘π π¦=γπ ππγ^(βπ) (sinβ‘π)+γπ ππγ^(β1) β(1βsin^2 π ) π¦=π+γπ ππγ^(β1) β(cos^2 π ) π¦=π+γπ ππγ^(β1) (cos π) π¦=π+γπ ππγ^(β1) (sinβ‘(π/2 βπ) ) π¦=π+ (π/2 βπ) ("As " γπ ππγ^(β1) (sinβ‘γΞΈ)γ=ΞΈ) (As cos ΞΈ = sin (π/2 β ΞΈ)) ("As " γπ ππγ^(β1) (sinβ‘γΞΈ)γ=ΞΈ) π¦=πβπ + π/2 π¦= π/2 Differentiating π€.π.π‘.π₯. ππ¦/ππ₯ = π(π/2)/ππ₯ π π/π π = 0 As derivative of constant is zero, here π/2 is a constant

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

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 You are here

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.