Ex 5.7, 2 - Find second order derivative x20 - Chapter 5 - Finding second order derivatives - Normal form

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.7, 2 Find the second order derivatives of the function 𝑥﷮20﷯ Let y = 𝑥﷮20﷯ Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑( 𝑥﷮20﷯)﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 20𝑥﷮20−1﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 20𝑥﷮19﷯ Again Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯﷯ = 𝑑 ( 20𝑥﷮19﷯)﷮𝑑𝑥﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯ = 20 𝑑( 𝑥﷮19﷯)﷮𝑑𝑥﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯ = 20 × 19 𝑥﷮19−1﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯ = 20 × 19 𝑥﷮18﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯ = 380 𝑥﷮18﷯ Thus, 𝒅﷮𝟐﷯𝒚﷮𝒅 𝒙﷮𝟐﷯﷯ = 380 𝒙﷮𝟏𝟖﷯

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