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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) = cos–1 𝑥 assuming it exists. Let y = cos–1 𝑥 cos⁡𝑦= 𝑥 𝑥 =cos⁡𝑦 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 (𝑑(𝑥))/𝑑𝑥 = (𝑑 (cos⁡𝑦 ))/𝑑𝑥 1 = (𝑑 (cos⁡𝑦 ))/𝑑𝑥 We need 𝑑𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (cos⁡𝑦 ))/𝑑𝑥 × 𝑑𝑦/𝑑𝑦 1 = −sin⁡𝑦 . 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/(− 𝒔𝒊𝒏⁡𝒚) 𝑑𝑦/𝑑𝑥 = (−1)/(√(𝟏 − 〖𝒄𝒐𝒔〗^𝟐⁡𝒚 ) " " ) We know that sin2 𝑦 + cos2 𝑦 = 1 sin2 𝑦 = 1 − cos2 𝑦 sin 𝑦 = √(1−cos^2⁡𝑦 ) Putting value of 𝑐𝑜𝑠⁡𝑦 = 𝑥 𝑑𝑦/𝑑𝑥 = (−1)/(√(1 − 𝒙^𝟐 ) " " ) As 𝑦 = cos^(−1) 𝑥 So, 𝑐𝑜𝑠⁡𝑦 = 𝑥 Hence, (𝒅(〖𝒄𝒐𝒔〗^(−𝟏)⁡〖𝒙)〗)/𝒅𝒙 = (−1)/(√(1 − 𝒙^𝟐 ) " " )

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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.