Misc 28 - Class 11
Last updated at May 29, 2018 by Teachoo
Transcript
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): 𝑥1 + 𝑡𝑎𝑛𝑥 Let f (x) = 𝑥1 + 𝑡𝑎𝑛𝑥 Let u = x & v = 1 + tan x So, f(x) = 𝑢𝑣 ∴ f’(x) = 𝑢𝑣′ Using quotient rule f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = x u’ = (x)’ = 1 & v = 1 + tan x v’ = (1 + tan x)’ = 0 + sec2 x = sec2 x Now, f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = 1(1 + tan𝑥) − 𝑠𝑒𝑐2 𝑥 (𝑥) (1 + tan𝑥)2 = 𝟏 + 𝒕𝒂𝒏𝒙 − 𝒙 𝒔𝒆𝒄𝟐 𝒙 (𝟏 + 𝒕𝒂𝒏𝒙)𝟐
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About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.