Example 40 (i) - Chapter 5 Class 12 Continuity and Differentiability (Important Question)

Last updated at Dec. 16, 2024 by Teachoo

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Example 40 (Method 1) Differentiate the following 𝑤.𝑟.𝑡. 𝑥. (i) cos^(−1) (sin⁡𝑥) Let 𝑓(𝑥) = cos^(−1) (sin⁡𝑥) 𝑓(𝑥) = cos^(−1) (〖cos 〗⁡(𝜋/2 −𝑥) ) 𝒇(𝒙) = 𝝅/𝟐 −𝒙 Differentiating 𝑤.𝑟.𝑡.𝑥 𝑓’(𝑥) = (𝑑 (𝜋/2))/𝑑𝑥 − (𝑑(𝑥))/𝑑𝑥 𝑓’(𝑥) = 0 − 1 𝒇’(𝒙) = − 1(𝐴𝑠 〖 𝑠𝑖𝑛 𝜃 〗⁡〖=〖𝑐𝑜𝑠 〗⁡〖(𝜋/2 −𝑥)〗〗 ) ("As " (𝑑(𝑥))/𝑑𝑥 " = 1 & " 𝜋/2 " is constant" ) Example 40 (Method 2) Differentiate the following 𝑤.𝑟.𝑡. 𝑥. (i) cos^(−1) (sin⁡𝑥) Let 𝑓(𝑥) = cos^(−1) (sin⁡𝑥) Differentiating 𝑤.𝑟.𝑡.𝑥 𝑓′(𝑥) = (−1)/√(1 − 〖(sin⁡𝑥)〗^2 ) × (sin⁡𝑥 )^′ 𝑓′(𝑥) = (−1)/√(1 − sin^2⁡𝑥 ) ×cos⁡𝑥 𝑓′(𝑥) = (−1)/√(cos^2⁡𝑥 ) ×cos⁡𝑥 𝑓′(𝑥) = (−1)/cos⁡𝑥 ×cos⁡𝑥 𝒇’(𝒙) = −1

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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