Ex 5.3, 10 - Chapter 5 Class 12 Continuity and Differentiability (Important Question)

Last updated at Dec. 16, 2024 by Teachoo

Ex 5.3, 10 - Find dy/dx in y=tan-1 (3x - x3/1 - 3x2) - Ex 5.3

Ex 5.3, 10 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Transcript

Ex 5.3, 10 Find 𝑑𝑦/𝑑𝑥 in, 𝑦 = tan–1 ((3𝑥− 𝑥^3)/( 1− 3𝑥2 )) , − 1/√3 < 𝑥 < 1/√3 𝑦 = tan–1 ((3𝑥− 𝑥^3)/( 1− 3𝑥2 )) Putting x = tan θ y = 〖𝑡𝑎𝑛〗^(−1) ((3 tan⁡〖𝜃 − tan⁡3 𝜃〗)/(1 − 3 tan⁡2 𝜃)) y = 〖𝑡𝑎𝑛〗^(−1) (tan⁡〖3 𝜃〗) 𝑦 = 3𝜃 Putting value of θ = 〖𝑡𝑎𝑛〗^(−1) 𝑥 𝑦 = 3〖 (𝑡𝑎𝑛〗^(−1) 𝑥) (𝑡𝑎𝑛⁡3θ " = " (3 𝑡𝑎𝑛⁡〖𝜃−𝑡𝑎𝑛⁡3 𝜃〗)/(1−3 𝑡𝑎𝑛⁡2 𝜃)) Since x = tan θ ∴ 〖𝑡𝑎𝑛〗^(−1) x = θ Differentiating both sides 𝑤.𝑟.𝑡.𝑥 . (𝑑(𝑦))/𝑑𝑥 = (𝑑 3〖(𝑡𝑎𝑛〗^(−1) 𝑥") " )/𝑑𝑥 𝑑𝑦/𝑑𝑥 =3 (𝑑〖(𝑡𝑎𝑛〗^(−1) 𝑥") " )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 3 (1/(1 + 𝑥^2 )) 𝒅𝒚/𝒅𝒙 = 𝟑/(𝟏 +〖 𝒙〗^𝟐 ) ((〖𝑡𝑎𝑛〗^(−1) 𝑥")‘ = " 1/(1 + 𝑥^2 ))

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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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