Question 6 - Examples - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 44 Differentiate w.r.t. x, the following function: (ii) 𝑒^(sec^2𝑥 ) + 3cos^(–1) 𝑥 Let y = 𝑒^(sec^2𝑥 ) + 3cos^(–1) 𝑥 Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑦/𝑑𝑥 = 𝑑(𝑒^(sec^2𝑥 )+ 3cos^(–1) 𝑥" " )/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 𝑑(𝑒^(sec^2𝑥 ) )/𝑑𝑥 + 𝒅(𝟑〖𝒄𝒐𝒔〗^(–𝟏) 𝒙)/𝒅𝒙 𝑑𝑦/𝑑𝑥 = 𝑒^(sec^2𝑥 ) 𝑑(sec^2𝑥 )/𝑑𝑥 + 3. ((−𝟏)/√(𝟏 −𝒙^𝟐 )) 𝑑𝑦/𝑑𝑥 = 𝑒^(sec^2𝑥 ). 2 sec 𝑥 . 𝒅(〖𝒔𝒆𝒄 〗𝒙 )/𝒅𝒙 − 3/√(1 −𝑥^2 ) "As" 𝑑(𝑒^𝑥 )/𝑑𝑥=𝑒^𝑥 & 𝑑(〖𝑐𝑜𝑠〗^(−1)𝑥 )/𝑑𝑥=(−1)/√(1 −〖 𝑥〗^2 ) 𝑑𝑦/𝑑𝑥 = 𝑒^(sec^2𝑥 ). 2 sec 𝑥 . 𝒔𝒆𝒄𝒙 .𝒕𝒂𝒏𝒙 − 3/√(1 − 𝑥^2 ) 𝒅𝒚/𝒅𝒙 = 〖𝟐 𝒆〗^(〖𝒔𝒆𝒄〗^𝟐𝒙 ). 〖𝒔𝒆𝒄〗^𝟐 𝒙 .𝒕𝒂𝒏𝒙 − 𝟑/√(𝟏 − 𝒙^𝟐 )
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo