Example 27 - Find derivative of f(x) = tan-1 x - Class 12 - Examples

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Example 27 Find the derivative of f given by f (x) = tan–1 π‘₯ assuming it exists. f (x) = tan–1 π‘₯ Let y = tan–1 π‘₯ tan⁑𝑦 = π‘₯ ∴ π‘₯ = tan⁑𝑦 Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ (𝑑(π‘₯))/𝑑π‘₯ = (𝑑 (tan⁑𝑦 ))/𝑑π‘₯ 1 = (𝑑 (tan⁑𝑦 ))/𝑑π‘₯ We need d𝑦 in denominator, so multiplying & Dividing by 𝑑𝑦. 1 = (𝑑 (tan⁑𝑦 ))/𝑑π‘₯ Γ— 𝑑𝑦/𝑑𝑦 1 = γ€–π¬πžπœγ€—^𝟐 π’š . 𝑑𝑦/𝑑π‘₯ 1 = (𝟏 + π’•π’‚π’πŸπ’š) 𝑑𝑦/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = 1/(1 + γ€–π­πšπ§γ€—^πŸβ‘π’š ) Putting π‘‘π‘Žπ‘›β‘π‘¦ = π‘₯ 𝑑𝑦/𝑑π‘₯ = 1/(1 + 𝒙^𝟐 ) As 𝑦 = tan^(βˆ’1) π‘₯ So, tan⁑𝑦 = π‘₯ Hence (𝒅(γ€–π­πšπ§γ€—^(βˆ’πŸ)⁑〖𝒙)γ€—)/𝒅𝒙 = 𝟏/(𝟏 + 𝒙^𝟐 )

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.