# Derivative of cot-1 x (cot 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) = cotโ1 ๐ฅ assuming it exists. Let y = cotโ1 ๐ฅ co๐กโก๐ฆ= ๐ฅ ๐ฅ =co๐กโก๐ฆ Differentiating both sides ๐ค.๐.๐ก.๐ฅ (๐(๐ฅ))/๐๐ฅ = (๐ (co๐กโก๐ฆ ))/๐ 1 = (๐ (co๐กโก๐ฆ ))/๐๐ฅ We need ๐๐ฆ in denominator, so multiplying & Dividing by ๐๐ฆ. 1 = (๐ (co๐กโก๐ฆ ))/๐๐ฅ ร ๐๐ฆ/๐๐ฆ 1 = โcosec^2โก๐ฆ . ๐๐ฆ/๐๐ฅ ๐๐ฆ/๐๐ฅ (โcosec^2โก๐ฆ ) = 1 ๐๐ฆ/๐๐ฅ = (โ1)/(ใ๐๐๐๐๐ใ^๐ ๐) ๐๐ฆ/๐๐ฅ = (โ1)/(๐ + ใ๐๐จ๐ญใ^๐โก๐) (๐ด๐ ใ ๐๐๐ ๐๐ใ^2โกใ๐ฆ= ใ1+ใโกใ๐๐๐กใ^2โก๐ฆ ใ) Putting ๐๐๐กโก๐ฆ = ๐ฅ ๐๐ฆ/๐๐ฅ = (โ1)/(๐^๐ + 1) As ๐ฆ = cot^(โ1) ๐ฅ So, ๐๐๐กโก๐ฆ = ๐ฅ Hence, (๐ (ใ๐๐จ๐ใ^(โ๐)โกใ๐)ใ)/๐ ๐ = (โ๐)/(๐^๐ + ๐)

Finding derivative of Inverse trigonometric functions

Derivative of cos-1 x (Cos inverse x)

Example 26

Example 27

Derivative of cot-1 x (cot inverse x) You are here

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.