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

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

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.