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

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