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

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

Miscellaneous 