Ex 5.3, 11 - Find dy/dx in, y = cos-1 (1 - x2 / 1 + x2) - Finding derivative of Inverse trigonometric functions

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.3, 11 Find 𝑑𝑦﷮𝑑𝑥﷯ in, 𝑦 = cos–1 1− 𝑥﷮2﷯﷮ 1+ 𝑥2 ﷯﷯ , 0 < x < 1 𝑦 = cos–1 1− 𝑥﷮2﷯﷮ 1+ 𝑥2 ﷯﷯ Putting x = tan θ y = 𝑐𝑜𝑠﷮−1﷯ 1− tan﷮2﷯𝜃﷮1+ tan﷮2﷯ 𝜃﷯﷯ y = cos−1 (cos 2𝜃) 𝑦 =2θ Putting value of θ = 𝑡𝑎𝑛﷮−1﷯ 𝑥 𝑦=2 ( 𝑡𝑎𝑛﷮−1﷯ 𝑥) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 . 𝑑(𝑦)﷮𝑑𝑥﷯ = 𝑑 (2 𝑡𝑎𝑛﷮−1﷯ 𝑥 ) ﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 2 𝑑 ( 𝑡𝑎𝑛﷮−1﷯ 𝑥 ) ﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 2 1﷮1+ 𝑥﷮2﷯﷯﷯ 𝒅𝒚﷮𝒅𝒙﷯ = 𝟐﷮𝟏+ 𝒙﷮𝟐﷯﷯

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