Question 6 - Examples - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Examples
Example 1
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Transcript
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 )
