Misc 18 - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
Last updated at Nov. 30, 2019 by
Last updated at Nov. 30, 2019 by
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
Derivatives by formula - sin & cos
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