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Ex 5.4, 5 - Differentiate log (cos e^x) - Teachoo - Ex 5.4

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Ex 5.4, 5 Differentiate w.r.t. x in , 〖log 〗⁡(cos⁡〖𝑒^𝑥 〗 )Let 𝑦 = 〖log 〗⁡(cos⁡〖𝑒^𝑥 〗 ) Differentiating both sides 𝑤.𝑟.𝑡.𝑥 𝑑(𝑦)/𝑑𝑥 = 𝑑(〖log 〗⁡(cos⁡〖𝑒^𝑥 〗 ) )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 1/cos⁡〖𝑒^𝑥 〗 . 𝑑(cos⁡〖𝑒^𝑥 〗 )/𝑑𝑥 = 1/cos⁡〖𝑒^𝑥 〗 . (−sin⁡〖𝑒^𝑥 〗 ) . 𝑑(𝑒^𝑥 )/𝑑𝑥 = 1/cos⁡〖𝑒^𝑥 〗 . (−sin⁡〖𝑒^𝑥 〗 ) . 𝑒^𝑥 = (−sin⁡〖𝑒^𝑥 〗)/cos⁡〖𝑒^𝑥 〗 . 𝑒^𝑥 = −tan⁡〖𝑒^𝑥 〗 . 𝑒^𝑥 = −𝒆^𝒙 . 𝒕𝒂𝒏⁡〖𝒆^𝒙 〗 (𝐴𝑠 𝑑/𝑑𝑥 (𝑙𝑜𝑔⁡𝑥 )= 1/𝑥) (𝐴𝑠 𝑑/𝑑𝑦 (cos⁡𝑥 )=〖−sin〗⁡𝑥 )

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.