Example 45 - Differentiate (i) cos-1 (sin x) - Chapter 5

 

 

 

Example 45 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

 

 

  1. Chapter 5 Class 12 Continuity and Differentiability (Term 1)
  2. Serial order wise

Transcript

Example 45 (Method 1) Differentiate the following 𝑀.π‘Ÿ.𝑑. π‘₯. (i) cos^(βˆ’1) (sin⁑π‘₯) Let 𝑓(π‘₯) = cos^(βˆ’1) (sin⁑π‘₯) 𝑓(π‘₯) = cos^(βˆ’1) (γ€–cos 〗⁑(πœ‹/2 βˆ’π‘₯) ) 𝒇(𝒙) = 𝝅/𝟐 βˆ’π’™ Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑓’(π‘₯) = (𝑑 (πœ‹/2))/𝑑π‘₯ βˆ’ (𝑑(π‘₯))/𝑑π‘₯ 𝑓’(π‘₯) = 0 βˆ’ 1 𝒇’(𝒙) = βˆ’ 1 (𝐴𝑠 γ€– 𝑠𝑖𝑛 πœƒ 〗⁑〖=γ€–π‘π‘œπ‘  〗⁑〖(πœ‹/2 βˆ’π‘₯)γ€— γ€— ) ("As " (𝑑(π‘₯))/𝑑π‘₯ " = 1 & " πœ‹/2 " is constant" ) Example 45 (Method 2) Differentiate the following 𝑀.π‘Ÿ.𝑑. π‘₯. (i) cos^(βˆ’1) (sin⁑π‘₯) Let 𝑓(π‘₯) = cos^(βˆ’1) (sin⁑π‘₯) Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑓′(π‘₯) = (βˆ’1)/√(1 βˆ’ γ€–(sin⁑π‘₯)γ€—^2 ) Γ— (sin⁑π‘₯ )^β€² 𝑓′(π‘₯) = (βˆ’1)/√(1 βˆ’ sin^2⁑π‘₯ ) Γ—cos⁑π‘₯ 𝑓′(π‘₯) = (βˆ’1)/√(cos^2⁑π‘₯ ) Γ—cos⁑π‘₯ 𝑓′(π‘₯) = (βˆ’1)/cos⁑π‘₯ Γ—cos⁑π‘₯ 𝒇’(𝒙) = βˆ’1

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.