Check Full Chapter Explained - Continuity and Differentiability - https://you.tube/Chapter-5-Class-12-Continuity  1. Chapter 5 Class 12 Continuity and Differentiability
2. Serial order wise
3. Ex 5.5

Transcript

Ex 5.5, 1 Differentiate the functions in, cos⁡𝑥 . cos⁡2𝑥 . cos⁡3𝑥 Let y = cos⁡𝑥 . cos⁡2𝑥 . cos⁡3𝑥 Taking log both sides log⁡𝑦 = log (cos⁡𝑥.cos⁡2𝑥.cos⁡3𝑥 ) log⁡𝑦 = log ⁡(cos⁡𝑥) + log ⁡(2𝑥) + log ⁡(cos⁡3𝑥) Differentiating both sides 𝑤.𝑟.𝑡.𝑥. 𝑑(log⁡𝑦 )/𝑑𝑥 = 𝑑(log ⁡(cos⁡𝑥)" + " log ⁡(2𝑥) "+ " log ⁡(cos⁡3𝑥))/𝑑𝑥 𝑑(log⁡𝑦 )/𝑑𝑥 (𝑑𝑦/𝑑𝑦) = (𝑑(log ⁡(cos⁡𝑥)) )/𝑑𝑥 + (𝑑(log ⁡(2𝑥)) )/𝑑𝑥 + (𝑑(log ⁡(cos⁡3𝑥)) )/𝑑𝑥 𝑑(log⁡𝑦 )/𝑑𝑦 (𝑑𝑦/𝑑𝑥) = 1/cos⁡𝑥 . (𝑑 (cos⁡𝑥 ))/𝑑𝑥 + 1/cos⁡2𝑥 . (𝑑(cos⁡2𝑥))/𝑑𝑥 + 1/cos⁡3𝑥 . 𝑑(cos⁡3𝑥 )/𝑑𝑥 1/𝑦 . 𝑑𝑦/𝑑𝑥 = 1/cos⁡𝑥 .(− sin⁡𝑥) + 1/cos⁡2𝑥 .(− sin⁡2𝑥).𝑑(2𝑥)/𝑑𝑥 + 1/cos⁡𝑥 .(− sin⁡3𝑥).𝑑(3𝑥)/𝑑𝑥 1/𝑦 . 𝑑𝑦/𝑑𝑥 = (−sin⁡𝑥)/cos⁡𝑥 − sin⁡2𝑥/cos⁡𝑥 . 2 − sin⁡3𝑥/cos⁡3𝑥 . 3 1/𝑦 . 𝑑𝑦/𝑑𝑥 = −tan⁡𝑥−tan⁡2𝑥. 2 −tan⁡3𝑥. 3 1/𝑦 . 𝑑𝑦/𝑑𝑥 = − (tan⁡𝑥+2 tan⁡2𝑥+3 tan⁡3𝑥 ) 𝑑𝑦/𝑑𝑥 = −𝑦 (tan⁡𝑥+2 tan⁡2𝑥+3 tan⁡3𝑥 ) 𝒅𝒚/𝒅𝒙 = − 𝒄𝒐𝒔⁡𝒙 . 𝒄𝒐𝒔⁡𝟐𝒙 . 𝒄𝒐𝒔⁡𝟑𝒙 (𝒕𝒂𝒏⁡𝒙+𝟐 𝒕𝒂𝒏⁡𝟐𝒙+𝟑 𝒕𝒂𝒏⁡𝟑𝒙 )

Ex 5.5 