# Derivative of cos-1 x (Cos 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) = cosβ1 π₯ assuming it exists. Let y = cosβ1 π₯ cosβ‘π¦= π₯ π₯ =cosβ‘π¦ Differentiating both sides π€.π.π‘.π₯ (π(π₯))/ππ₯ = (π (cosβ‘π¦ ))/ππ₯ 1 = (π (cosβ‘π¦ ))/ππ₯ We need ππ¦ in denominator, so multiplying & Dividing by ππ¦. 1 = (π (cosβ‘π¦ ))/ππ₯ Γ ππ¦/ππ¦ 1 = βsinβ‘π¦ . ππ¦/ππ₯ ππ¦/ππ₯ = 1/(β πππβ‘π) ππ¦/ππ₯ = (β1)/(β(π β γπππγ^πβ‘π ) " " ) We know that sin2 π¦ + cos2 π¦ = 1 sin2 π¦ = 1 β cos2 π¦ sin π¦ = β(1βcos^2β‘π¦ ) Putting value of πππ β‘π¦ = π₯ ππ¦/ππ₯ = (β1)/(β(1 β π^π ) " " ) As π¦ = cos^(β1) π₯ So, πππ β‘π¦ = π₯ Hence, (π (γπππγ^(βπ)β‘γπ)γ)/π π = (β1)/(β(1 β π^π ) " " )

Finding derivative of Inverse trigonometric functions

Derivative of cos-1 x (Cos inverse x)
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Example 26

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, 9

Ex 5.3, 12

Ex 5.3, 14 Important

Ex 5.3, 11

Ex 5.3, 13

Ex 5.3, 10 Important

Ex 5.3, 15

Misc 5

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.