# Derivative of sec-1 x (Sec inverse x)

Last updated at April 8, 2019 by Teachoo

Last updated at April 8, 2019 by Teachoo

Transcript

Find the derivative of f given by f (x) = secβ1 π₯ assuming it exists. Let π¦ = sec^(β1) π₯ π ππβ‘π¦= π₯ π₯ =π ππβ‘π¦ Differentiating both sides π€.π.π‘.π₯ ππ₯/ππ₯ = (π (π ππβ‘π¦ ))/ππ₯ 1 = (π (π ππβ‘π¦ ))/ππ₯ We need ππ¦ in denominator, so multiplying & Dividing by ππ¦. 1 = (π (secβ‘π¦ ))/ππ₯ Γ ππ¦/ππ¦ 1 = tanβ‘π¦ .secβ‘π¦ . ππ¦/ππ₯ ππ¦/ππ₯ tanβ‘π¦ .secβ‘π¦= 1 ππ¦/ππ₯ = 1/(πππβ‘π .γ secγβ‘π¦ ) ππ¦/ππ₯ = 1/((β(γπ¬ππγ^πβ‘π β π)) .γ secγβ‘π¦ ) Putting value of π ππβ‘π¦ = π₯ ππ¦/ππ₯ = 1/((β(π₯^2 β 1 ) ) . π₯) ππ¦/ππ₯ = 1/(π₯ β(π₯^2 β 1 ) ) As π¦ = sec^(β1) π₯ So, π ππβ‘π¦ = π₯ Hence π (γπππγ^(βπ) π)/π π = π/(π β(π^π β π ) ) As tan2 ΞΈ = sec2 ΞΈ β 1, tan ΞΈ = β("sec2 ΞΈ β 1" )

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Example 27

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Ex 5.3, 9

Ex 5.3, 12 Important

Ex 5.3, 14 Important

Ex 5.3, 11 Important

Ex 5.3, 13

Ex 5.3, 10 Important

Ex 5.3, 15 Important

Misc 5 Important

Misc 4

Misc 13

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.