Misc 18 - Find derivative: sec x - 1 / sec x + 1 - CBSE - Derivatives by formula - sin & cos

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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) = So, f (x) = Using quotient rule f (x) = 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 f (x) = = 2 = ( sec tan ) ( sec + 1) ( sec tan ) ( sec 1) ( sec x + 1 ) 2 = sec . tan [( sec + 1) ( sec 1)] ( sec x + 1 ) 2 = sec . tan ( sec + 1 sec + 1 ) ( sec x + 1 ) 2 = sec . tan (1 + 1 + sec sec ) ( sec x + 1 ) 2 = sec tan (2 + 0) ( sec + 1 ) 2 = 2 sec tan ( sec + 1 ) 2 Hence f (x) = ( + )

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