# Ex 5.7, 3 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.7, 3 Find the second order derivatives of the function 𝑥. cos𝑥 Let y = 𝑥. cos𝑥 Differentiating 𝑤.𝑟.𝑡.𝑥 . 𝑑𝑦𝑑𝑥 = 𝑑(𝑥. cos𝑥)𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑑 𝑥𝑑𝑥 . cos𝑥 + 𝑑( cos𝑥)𝑑𝑥 . 𝑥 𝑑𝑦𝑑𝑥 = cos𝑥+(− sin𝑥 ) . 𝑥 𝑑𝑦𝑑𝑥 = cos𝑥 − 𝑥 sin𝑥 Again Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑑 (cos𝑥 − 𝑥 sin𝑥)𝑑𝑥 𝑑2𝑦𝑑 𝑥2 = 𝑑( cos𝑥)𝑑𝑥 − 𝑑( x sin𝑥)𝑑𝑥 Using product rule in 𝑥 𝑠𝑖𝑛𝑥 𝑑2𝑦𝑑 𝑥2 = − sin𝑥 − 𝑑 𝑥𝑑𝑥. sin𝑥+ 𝑑 sin𝑥𝑑𝑥.𝑥 𝑑2𝑦𝑑 𝑥2 = − sin𝑥 − sin𝑥+ cos𝑥 . 𝑥 𝑑2𝑦𝑑 𝑥2 = − sin𝑥 − sin𝑥− x cos𝑥 𝒅𝟐𝒚𝒅 𝒙𝟐 = − 𝒙 𝒄𝒐𝒔𝒙−𝟐 𝒔𝒊𝒏𝒙

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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.