# Ex 5.4, 9 - 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 5.4, 9 Differentiate w.r.t. x in, cos𝑥 log𝑥 , x > 2 Let 𝑦 = cos𝑥 log𝑥 Let 𝑢 = cos𝑥 & 𝑣 = log𝑥 ∴ 𝑦 = 𝑢𝑣 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑 𝑦𝑑𝑥 = 𝑑 𝑢𝑣𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑢′𝑣 − 𝑣 ′𝑢 𝑣2 𝑑𝑦𝑑𝑥 = cos𝑥′ log𝑥 − log𝑥 . cos𝑥 log𝑥2 𝑑𝑦𝑑𝑥 = − sin𝑥 . log𝑥 − 1 𝑥 . cos𝑥 log𝑥2 𝑑𝑦𝑑𝑥 = − sin𝑥 . log𝑥 + 1 𝑥 . cos𝑥 log𝑥2 𝑑𝑦𝑑𝑥 = − 𝑥 sin𝑥 log𝑥 + cos𝑥𝑥 log𝑥2 𝒅𝒚𝒅𝒙 = − 𝒙 𝒔𝒊𝒏𝒙 𝒍𝒐𝒈𝒙 + 𝒄𝒐𝒔𝒙𝒙 𝒍𝒐𝒈𝒙𝟐

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