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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Concept wise

Transcript

Find the derivative of f given by f (x) = cot–1 𝑥 assuming it exists. Let y = cot–1 𝑥 co𝑡⁡𝑦= 𝑥 𝑥 =co𝑡⁡𝑦 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 (𝑑(𝑥))/𝑑𝑥 = (𝑑 (co𝑡⁡𝑦 ))/𝑑 1 = (𝑑 (co𝑡⁡𝑦 ))/𝑑𝑥 We need 𝑑𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (co𝑡⁡𝑦 ))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦 1 = −cosec^2⁡𝑦 . 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥 (−cosec^2⁡𝑦 ) = 1 𝑑𝑦/𝑑𝑥 = (−1)/(〖𝒄𝒐𝒔𝒆𝒄〗^𝟐 𝒚) 𝑑𝑦/𝑑𝑥 = (−1)/(𝟏 + 〖𝐜𝐨𝐭〗^𝟐⁡𝒚) (𝐴𝑠 〖 𝑐𝑜𝑠𝑒𝑐〗^2⁡〖𝑦= 〖1+〗⁡〖𝑐𝑜𝑡〗^2⁡𝑦 〗) Putting 𝑐𝑜𝑡⁡𝑦 = 𝑥 𝑑𝑦/𝑑𝑥 = (−1)/(𝒙^𝟐 + 1) As 𝑦 = cot^(−1) 𝑥 So, 𝑐𝑜𝑡⁡𝑦 = 𝑥 Hence, (𝒅(〖𝐜𝐨𝒕〗^(−𝟏)⁡〖𝒙)〗)/𝒅𝒙 = (−𝟏)/(𝒙^𝟐 + 𝟏)

About the Author

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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.