Misc 29 - Find derivative: (x + sec x) (x - tan x) - Miscellaneous

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Misc 29 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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

Transcript

Misc 29 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): (x + sec x) (x – tan x) Let f(x) = (x + sec x) (x – tan x) Let u = x + sec x & v = x – tan x ∴ f(x) = uv So, f’(x) = (𝑢𝑣)^′ Using product rule f’(x) = 𝑢^′ 𝑣+〖 𝑣〗^′ 𝑢 Finding u’ & v’ u = x + sec x u’ = (x + sec x)’ = 1 + sec x tan x & v = x – tan x v’ = (x – tan x)’ = 1 – sec2 x Now, f’(x) = (𝑢𝑣)′ = 𝑢^′ 𝑣+〖 𝑣〗^′ 𝑢 = (1 + sec x tan x) (x – tan x) + (1 – sec2 x) (x + sec x) = (x + sec x) (1 – sec2 x) + (x – tan x) (1 + sec x tan x) Derivative of x = 1 Derivative of sec x = sec x tan x Derivative of x = 1 Derivative of tan x = sec2 x

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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.