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  1. Chapter 5 Class 12 Continuity and Differentiability
  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 Put π‘₯ = π‘ π‘–π‘›β‘πœƒ 𝑦=〖𝑠𝑖𝑛〗^(βˆ’πŸ) (sinβ‘πœƒ)+〖𝑠𝑖𝑛〗^(βˆ’1) √(1βˆ’sin^2 πœƒ ) 𝑦=πœƒ+〖𝑠𝑖𝑛〗^(βˆ’1) √(cos^2 πœƒ ) 𝑦=πœƒ+〖𝑠𝑖𝑛〗^(βˆ’1) (cos πœƒ) 𝑦=πœƒ+〖𝑠𝑖𝑛〗^(βˆ’1) (sin⁑(πœ‹/2 βˆ’πœƒ) ) 𝑦=πœƒ+ (πœ‹/2 βˆ’πœƒ) ("As " 〖𝑠𝑖𝑛〗^(βˆ’1) (sin⁑〖θ)γ€—=ΞΈ) (As cos ΞΈ = sin (πœ‹/2 – ΞΈ)) ("As " 〖𝑠𝑖𝑛〗^(βˆ’1) (sin⁑〖θ)γ€—=ΞΈ) 𝑦=πœƒβˆ’πœƒ + πœ‹/2 𝑦= πœ‹/2 Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯. 𝑑𝑦/𝑑π‘₯ = 𝑑(πœ‹/2)/𝑑π‘₯ π’…π’š/𝒅𝒙 = 0 As derivative of constant is zero, here πœ‹/2 is a constant

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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.