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Ex 5.3, 9 - Find dy/dx in y=sin-1 (2x / 1 + 2x2) - Ex 5.3

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.3, 9 Find 𝑑𝑦﷮𝑑𝑥﷯ in, y = sin﷮−1﷯ 2𝑥﷮ 1+2𝑥2 ﷯﷯ 𝑦 = sin﷮−1﷯ 2𝑥﷮ 1+2𝑥2 ﷯﷯ Putting x = tan θ 𝑦 = sin﷮−1﷯ 2𝑥﷮ 1 + 𝑥2 ﷯﷯ 𝑦 = sin﷮−1﷯ 2 𝑡𝑎𝑛﷮𝜃﷯﷮1+ 𝑡𝑎𝑛﷮2﷯𝜃﷯﷯ 𝑦 = sin﷮−1﷯ ( sin⁡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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