# Example 26 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Jan. 3, 2020 by Teachoo

Last updated at Jan. 3, 2020 by Teachoo

Transcript

Example 26 Find the derivative of f given by π (π₯)=γπ ππγ^(β1) π₯ assuming it exists. π (π₯)=γπ ππγ^(β1) π₯ Let π¦= γπ ππγ^(β1) π₯ sinβ‘γπ¦=π₯γ π₯=sinβ‘γπ¦ γ Differentiating both sides π€.π.π‘.π₯ ππ₯/ππ₯ = (π (sinβ‘π¦ ))/ππ₯ 1 = (π (sinβ‘π¦ ))/ππ₯ Γ ππ¦/ππ¦ 1 = (π (sinβ‘π¦ ))/ππ¦ Γ ππ¦/ππ₯ 1 = cosβ‘π¦ ππ¦/ππ₯ 1/cosβ‘π¦ =ππ¦/ππ₯ ππ¦/ππ₯ = 1/πππβ‘π ππ¦/ππ₯= 1/β(π β γπππγ^π π) Putting π ππβ‘γπ¦=π₯γ ππ¦/ππ₯= 1/β(1 β π^π ) Hence, (π (γπππγ^(βπ) π" " ))/π π = π/β(π β π^π ) "We know that" γπ ππγ^2 π+γπππ γ^2 π=1 γπππ γ^2=1βγπ ππγ^2 π cosβ‘π=β(1βγπ ππγ^2 π) " " As π¦ = γπ ππγ^(β1) π₯ So, π ππβ‘π¦ = π₯

Finding derivative of Inverse trigonometric functions

Derivative of cos-1 x (Cos inverse x)

Example 26 Important You are here

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

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.