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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Ex 5.5, 1 Differentiate the functions in, cos⁑π‘₯ . cos⁑2π‘₯ . cos⁑3π‘₯ Let y = cos⁑π‘₯ . cos⁑2π‘₯ . cos⁑3π‘₯ Taking log both sides log⁑𝑦 = log (cos⁑π‘₯.cos⁑2π‘₯.cos⁑3π‘₯ ) log⁑𝑦 = log ⁑(cos⁑π‘₯) + log ⁑(2π‘₯) + log ⁑(cos⁑3π‘₯) Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯. 𝑑(log⁑𝑦 )/𝑑π‘₯ = 𝑑(log ⁑(cos⁑π‘₯)" + " log ⁑(2π‘₯) "+ " log ⁑(cos⁑3π‘₯))/𝑑π‘₯ 𝑑(log⁑𝑦 )/𝑑π‘₯ (𝑑𝑦/𝑑𝑦) = (𝑑(log ⁑(cos⁑π‘₯)) )/𝑑π‘₯ + (𝑑(log ⁑(2π‘₯)) )/𝑑π‘₯ + (𝑑(log ⁑(cos⁑3π‘₯)) )/𝑑π‘₯ 𝑑(log⁑𝑦 )/𝑑𝑦 (𝑑𝑦/𝑑π‘₯) = 1/cos⁑π‘₯ . (𝑑 (cos⁑π‘₯ ))/𝑑π‘₯ + 1/cos⁑2π‘₯ . (𝑑(cos⁑2π‘₯))/𝑑π‘₯ + 1/cos⁑3π‘₯ . 𝑑(cos⁑3π‘₯ )/𝑑π‘₯ 1/𝑦 . 𝑑𝑦/𝑑π‘₯ = 1/cos⁑π‘₯ .(βˆ’ sin⁑π‘₯) + 1/cos⁑2π‘₯ .(βˆ’ sin⁑2π‘₯).𝑑(2π‘₯)/𝑑π‘₯ + 1/cos⁑π‘₯ .(βˆ’ sin⁑3π‘₯).𝑑(3π‘₯)/𝑑π‘₯ 1/𝑦 . 𝑑𝑦/𝑑π‘₯ = (βˆ’sin⁑π‘₯)/cos⁑π‘₯ βˆ’ sin⁑2π‘₯/cos⁑π‘₯ . 2 βˆ’ sin⁑3π‘₯/cos⁑3π‘₯ . 3 1/𝑦 . 𝑑𝑦/𝑑π‘₯ = βˆ’tan⁑π‘₯βˆ’tan⁑2π‘₯. 2 βˆ’tan⁑3π‘₯. 3 1/𝑦 . 𝑑𝑦/𝑑π‘₯ = βˆ’ (tan⁑π‘₯+2 tan⁑2π‘₯+3 tan⁑3π‘₯ ) 𝑑𝑦/𝑑π‘₯ = βˆ’π‘¦ (tan⁑π‘₯+2 tan⁑2π‘₯+3 tan⁑3π‘₯ ) π’…π’š/𝒅𝒙 = βˆ’ 𝒄𝒐𝒔⁑𝒙 . π’„π’π’”β‘πŸπ’™ . π’„π’π’”β‘πŸ‘π’™ (𝒕𝒂𝒏⁑𝒙+𝟐 π’•π’‚π’β‘πŸπ’™+πŸ‘ π’•π’‚π’β‘πŸ‘π’™ )

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.