Misc 13 - Find dy/dx, if y = sin-1 x + sin-1 root 1-x2 - Miscellaneous

Misc  13 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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

Transcript

Misc 13 Find 𝑑𝑦/𝑑π‘₯ , if 𝑦=〖𝑠𝑖𝑛〗^(βˆ’πŸ) π‘₯+〖𝑠𝑖𝑛〗^(βˆ’1) √(1βˆ’π‘₯2), – 1 ≀ π‘₯ ≀ 1 𝑦=〖𝑠𝑖𝑛〗^(βˆ’πŸ) π‘₯+〖𝑠𝑖𝑛〗^(βˆ’1) √(1βˆ’π‘₯^2 ) , – 1 ≀ π‘₯ ≀ 1 Putting 𝒙 = π’”π’Šπ’β‘πœ½ 𝑦=〖𝑠𝑖𝑛〗^(βˆ’πŸ) (sinβ‘πœƒ)+〖𝑠𝑖𝑛〗^(βˆ’1) √(1βˆ’sin^2 πœƒ ) 𝑦=𝜽+〖𝑠𝑖𝑛〗^(βˆ’1) √(γ€–πœπ¨π¬γ€—^𝟐 πœƒ ) 𝑦=πœƒ+〖𝑠𝑖𝑛〗^(βˆ’1) (cos πœƒ) 𝑦=πœƒ+〖𝑠𝑖𝑛〗^(βˆ’1) (sin⁑(𝝅/𝟐 βˆ’πœ½) ) 𝑦=πœƒ+ (πœ‹/2 βˆ’πœƒ) 𝑦=πœƒβˆ’πœƒ + πœ‹/2 π’š= 𝝅/𝟐 Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯. 𝑑𝑦/𝑑π‘₯ = 𝑑(πœ‹/2)/𝑑π‘₯ π’…π’š/𝒅𝒙 = 0

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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.