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Misc 28 - Find derivative: x / 1 + tan x - Chapter 13 Class 11

Misc 28 - Chapter 13 Class 11 Limits and Derivatives - Part 2
Misc 28 - Chapter 13 Class 11 Limits and Derivatives - Part 3

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Misc 28 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): π‘₯/(1 + π‘‘π‘Žπ‘›β‘π‘₯ ) Let f (x) = π‘₯/(1 + π‘‘π‘Žπ‘›β‘π‘₯ ) Let u = x & v = 1 + tan x So, f(x) = 𝑒/𝑣 ∴ f’(x) = (𝑒/𝑣)^β€² Using quotient rule f’(x) = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 Finding u’ & v’ u = x u’ = 1 & v = 1 + tan x v’ = (1 + tan x)’ = 0 + sec2 x = sec2 x Now, f’(x) = (𝑒/𝑣)^β€² = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 = (1(1 +γ€– tan〗⁑〖π‘₯)γ€— βˆ’ 𝑠𝑒𝑐2 π‘₯ (π‘₯))/γ€–(1 +γ€– tan〗⁑〖π‘₯)γ€—γ€—^2 = (𝟏 +γ€– 𝒕𝒂𝒏〗⁑〖𝒙 βˆ’ 𝒙 π’”π’†π’„πŸ 𝒙〗)/γ€–(𝟏 +γ€– 𝒕𝒂𝒏〗⁑〖𝒙)γ€—γ€—^𝟐 = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 = (1(1 +γ€– tan〗⁑〖π‘₯)γ€— βˆ’ 𝑠𝑒𝑐2 π‘₯ (π‘₯))/γ€–(1 +γ€– tan〗⁑〖π‘₯)γ€—γ€—^2 = (𝟏 +γ€– 𝒕𝒂𝒏〗⁑〖𝒙 βˆ’ 𝒙 π’”π’†π’„πŸ 𝒙〗)/γ€–(𝟏 +γ€– 𝒕𝒂𝒏〗⁑〖𝒙)γ€—γ€—^𝟐

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.