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  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise

Transcript

Misc 18 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): sec⁡〖x − 1〗/sec⁡〖x + 1〗 Let f (x) = sec⁡〖x − 1〗/sec⁡〖x + 1〗 Let u = sec x – 1 & v = sec x + 1 ∴ f(x) = 𝑢/𝑣 So, f’(x) = (𝑢/𝑣)^′ Using quotient rule f’(x) = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 Finding u’ & v’ u = sec x – 1 u’ = (sec x – 1)’ = sec x tan x – 0 = sec x tan x & v = sec x + 1 v’= sec x tan x + 0 = sec x tan x Now, f’(x) = (𝑢/𝑣)^′ Derivative of sec x = sec x tan x Derivative of constant = 0 = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 = ( (sec⁡〖𝑥 tan⁡〖𝑥)〗 (sec⁡〖𝑥 + 1) − (sec⁡〖𝑥 tan⁡〖𝑥)〗 (sec⁡〖𝑥 − 1)〗 〗 〗 〗)/〖(sec⁡〖x + 1〗)〗^2 = ( sec⁡〖𝑥 . tan⁡𝑥 [(sec⁡〖𝑥 + 1) − (sec⁡〖𝑥 − 1)] 〗 〗 〗)/〖(sec⁡〖x + 1〗)〗^2 = ( sec⁡〖𝑥 . tan⁡𝑥 (sec⁡〖𝑥 + 1−〖 sec〗⁡〖𝑥 + 1〗) 〗 〗)/〖(sec⁡〖x + 1〗)〗^2 = sec⁡〖𝑥 tan⁡〖𝑥 (2 + 0)〗 〗/〖(sec⁡〖𝑥 + 1〗)〗^2 = (𝟐 𝐬𝐞𝐜⁡〖𝒙 𝐭𝐚𝐧⁡𝒙 〗)/〖(𝒔𝒆𝒄⁡〖𝒙 + 𝟏〗)〗^𝟐

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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.