Misc 29 - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo