Ex 5.7, 4 - Chapter 5 Class 12 Continuity and Differentiability

Transcript

Ex 5.7, 4 Find the second order derivatives of the function log﷮𝑥﷯ Let y = log﷮𝑥﷯ Differentiating 𝑤.𝑟.𝑡.𝑥 . 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑( log﷮𝑥﷯)﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 1﷮𝑥﷯ Again Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯﷯ = 𝑑 ﷮𝑑𝑥﷯ 1﷮𝑥﷯﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯ = 𝑑( 𝑥﷮−1﷯)﷮𝑑𝑥﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯ = −1 𝑥﷮−1−1﷯ 𝑑﷮2﷯𝑦﷮𝑑 𝑥﷮2﷯﷯ = 𝑥﷮−2﷯ 𝒅﷮𝟐﷯𝒚﷮𝒅 𝒙﷮𝟐﷯﷯ = −𝟏﷮ 𝒙﷮𝟐﷯﷯