If 𝑦 = sin -1 x, then (1-x 2 ) y 2 𝑖𝑠 equal to

(a) xy 1  

(b) 𝑥𝑦 

(c) xy 2  

(d) x 2

 

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Question 16 If 𝑦 = 〖𝑠𝑖𝑛〗^(−1) 𝑥, then (1−𝑥^2 ) 𝑦_2 𝑖𝑠 equal to (a) 〖𝑥𝑦〗_1 (b) 𝑥𝑦 (c) 〖𝑥𝑦〗_2 (d) 𝑥^2 Given 𝑦 = 〖𝑠𝑖𝑛〗^(−1) 𝑥 Differentiating w.r.t x 𝑑𝑦/𝑑𝑥=𝑑(sin^(−1)⁡𝑥 )/𝑥 𝒅𝒚/𝒅𝒙=𝟏/√(𝟏 − 𝒙^𝟐 ) 𝑦^′=1/√(1 − 𝑥^2 ) 𝒚^′ × √(𝟏 − 𝒙^𝟐 )=𝟏 Again differentiating w.r.t x (𝑦^′ × √(1 − 𝑥^2 ))^′=𝑑(1)/𝑑𝑥 (𝑦^′ × √(1 − 𝑥^2 ))^′=0 〖𝒚^′′ √(𝟏 − 𝒙^𝟐 )+𝒚^′ (√(𝟏 − 𝒙^𝟐 ))〗^′=𝟎 〖𝑦^′′ √(1 − 𝑥^2 )+𝑦^′ ×1/(2√(1 − 𝑥^2 )) (1 − 𝑥^2 )〗^′=0 𝑦^′′ √(1 − 𝑥^2 )+𝑦^′ ×1/(2√(1 − 𝑥^2 )) × −2𝑥=0 𝑦^′′ √(1 − 𝑥^2 )−𝑦^′ ×𝑥/√(1 − 𝑥^2 ) =0 𝑦^′′ √(1 − 𝑥^2 )=𝑦^′ ×𝑥/√(1 − 𝑥^2 ) 𝑦^′′ √(1 − 𝑥^2 ) ×√(1 − 𝑥^2 )=𝑦^′ 𝑥 𝒚^′′ (𝟏 − 𝒙^𝟐) =𝒚^′ 𝒙 So, the correct answer is (a)

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.