# Misc 18 - Chapter 13 Class 11 Limits and Derivatives

Last updated at Nov. 30, 2019 by Teachoo

Last updated at Nov. 30, 2019 by Teachoo

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 . tan𝑥 [(sec〖𝑥 + 1) − (sec〖𝑥 − 1)] 〗 〗 〗)/〖(sec〖x + 1〗)〗^2 = ( sec〖𝑥 . tan𝑥 (sec〖𝑥 + 1−〖 sec〗〖𝑥 + 1〗) 〗 〗)/〖(sec〖x + 1〗)〗^2 = sec〖𝑥 tan〖𝑥 (2 + 0)〗 〗/〖(sec〖𝑥 + 1〗)〗^2 = (𝟐 𝐬𝐞𝐜〖𝒙 𝐭𝐚𝐧𝒙 〗)/〖(𝒔𝒆𝒄〖𝒙 + 𝟏〗)〗^𝟐

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.