# Ex 5.5, 1 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 5.5, 1 Differentiate the functions in, cos𝑥 . cos2𝑥 . cos3𝑥 Let y = cos𝑥 . cos2𝑥 . cos3𝑥 Taking log both sides log𝑦 = log cos𝑥. cos2𝑥. cos3𝑥 log𝑦 = log (cos𝑥) + log (2𝑥) + log (cos3𝑥) Differentiating both sides 𝑤.𝑟.𝑡.𝑥. 𝑑 log𝑦𝑑𝑥 = 𝑑 log (cos𝑥) + log (2𝑥) + log ( cos3𝑥)𝑑𝑥 𝑑 log𝑦𝑑𝑥 𝑑𝑦𝑑𝑦 = 𝑑 log (cos𝑥) 𝑑𝑥 + 𝑑 log (2𝑥) 𝑑𝑥 + 𝑑 log ( cos3𝑥) 𝑑𝑥 𝑑 log𝑦𝑑𝑦 𝑑𝑦𝑑𝑥 = 1 cos𝑥 . 𝑑 cos𝑥𝑑𝑥 + 1 cos2𝑥 . 𝑑( cos2𝑥)𝑑𝑥 + 1 cos3𝑥 . 𝑑 cos3𝑥𝑑𝑥 1𝑦 . 𝑑𝑦𝑑𝑥 = 1 cos𝑥 .(− sin𝑥) + 1 cos2𝑥 .(− sin2𝑥). 𝑑 2𝑥𝑑𝑥 + 1 cos𝑥.(− sin3𝑥). 𝑑 3𝑥𝑑𝑥 1𝑦 . 𝑑𝑦𝑑𝑥 = − sin𝑥 cos𝑥 − sin2𝑥 cos𝑥 . 2 − sin3𝑥 cos3𝑥. 3 1𝑦 . 𝑑𝑦𝑑𝑥 = − tan𝑥− tan2𝑥. 2 − tan3𝑥. 3 1𝑦 . 𝑑𝑦𝑑𝑥 = − tan𝑥+2 tan2𝑥+3 tan3𝑥 𝑑𝑦𝑑𝑥 = −𝑦 tan𝑥+2 tan2𝑥+3 tan3𝑥 𝒅𝒚𝒅𝒙 = − 𝒄𝒐𝒔𝒙 . 𝒄𝒐𝒔𝟐𝒙 . 𝒄𝒐𝒔𝟑𝒙 𝒕𝒂𝒏𝒙+𝟐 𝒕𝒂𝒏𝟐𝒙+𝟑 𝒕𝒂𝒏𝟑𝒙

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Davneet Singh

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.