# Ex 5.7, 10

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 5.7, 10 Find the second order derivatives of the function sin ( log𝑥) Let y = sin ( log𝑥) Differentiating 𝑤.𝑟.𝑡.𝑥 . 𝑑𝑦𝑑𝑥 = 𝑑( sin ( log𝑥))𝑑𝑥 𝑑𝑦𝑑𝑥 = cos(log𝑥) . 𝑑( log𝑥)𝑑𝑥 𝑑𝑦𝑑𝑥 = cos(log𝑥) . 1𝑥 𝑑𝑦𝑑𝑥 = cos(log𝑥)𝑥 Again Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑑𝑑𝑥 cos(log𝑥)𝑥 𝑑2𝑦𝑑 𝑥2 = 𝑑𝑑𝑥 cos(log𝑥)𝑥 𝑑2𝑦𝑑 𝑥2 = 𝑑(cos(log𝑥))𝑑𝑥 . 𝑥 − 𝑑 𝑥𝑑𝑥 . cos(log𝑥) 𝑥2 𝑑2𝑦𝑑 𝑥2 = − sin log𝑥 . 𝑑 log𝑥𝑑𝑥 . 𝑥 −1 . cos(log𝑥) 𝑥2 𝑑2𝑦𝑑 𝑥2 = − sin log𝑥 . 1𝑥 . 𝑥 − cos (log𝑥) 𝑥2 𝑑2𝑦𝑑 𝑥2 = − sin log𝑥 − cos(log𝑥) 𝑥2 𝒅𝟐𝒚𝒅 𝒙𝟐 = − 𝒔𝒊𝒏 𝒍𝒐𝒈𝒙 + 𝒄𝒐𝒔(𝒍𝒐𝒈𝒙) 𝒙𝟐

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.