Ex 5.4, 9 - Differentiate cos x / log x - Chapter 5 NCERT - Ex 5.4

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.4, 9 Differentiate w.r.t. x in, cos﷮𝑥﷯﷮ log﷮𝑥﷯﷯ , x > 2 Let 𝑦 = cos﷮𝑥﷯﷮ log﷮𝑥﷯﷯ Let 𝑢 = cos﷮𝑥﷯ & 𝑣 = log﷮𝑥﷯ ∴ 𝑦 = 𝑢﷮𝑣﷯ Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑 𝑦﷯﷮𝑑𝑥﷯ = 𝑑 𝑢﷮𝑣﷯﷯﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑢﷮′﷯𝑣 − 𝑣 ﷮′﷯𝑢﷮ 𝑣﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = cos﷮𝑥﷯﷯﷮′﷯ log﷮𝑥﷯ − log﷮𝑥﷯﷯ . cos﷮𝑥﷯﷮ log﷮𝑥﷯﷯﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − sin﷮𝑥﷯ . log﷮𝑥﷯ − 1 ﷮𝑥﷯ . cos﷮𝑥﷯﷮ log﷮𝑥﷯﷯﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − sin﷮𝑥﷯ . log﷮𝑥﷯ + 1 ﷮𝑥﷯ . cos﷮𝑥﷯﷯﷮ log﷮𝑥﷯﷯﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − 𝑥 sin﷮𝑥 log﷮𝑥 + cos﷮𝑥﷯﷯﷯﷮𝑥﷯﷮ log﷮𝑥﷯﷯﷮2﷯﷯﷯ 𝒅𝒚﷮𝒅𝒙﷯ = − 𝒙 𝒔𝒊𝒏﷮𝒙 𝒍𝒐𝒈﷮𝒙 + 𝒄𝒐𝒔﷮𝒙﷯﷯﷯﷮𝒙 𝒍𝒐𝒈﷮𝒙﷯﷯﷮𝟐﷯﷯﷯

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.