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Misc 1 (ii) - Chapter 12 Class 11 Limits and Derivatives

Last updated at May 29, 2023 by

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Misc 1 Find the derivative of the following functions from first principle: (ii) (−𝑥)^(−1) Let f (x) = (−𝑥)^(−1) We need to find Derivative of f(x) i.e. f’ (x) We know that f’(x) = lim┬(h→0) f⁡〖(x + h) − f(x)〗/h Here, f (x) = (−𝑥)^(−1) So, f (x + h) = (−(𝑥+ℎ))^(−1) Putting values f’(x) = lim┬(h→0)⁡〖(〖(−(𝑥 + ℎ)) 〗^(−1) 〖− (− 𝑥)〗^(−1))/ℎ〗 = lim┬(h→0)⁡〖((1/(−(𝑥 + ℎ))) −(1/(−𝑥)))/ℎ〗 = lim┬(h→0)⁡〖((−1)/(𝑥 + ℎ) + 1/𝑥)/ℎ〗 = lim┬(h→0)⁡〖((− 𝑥 + 𝑥 + ℎ)/(𝑥 (𝑥 + ℎ) ))/ℎ〗 = lim┬(h→0)⁡〖(− 𝑥 + 𝑥 + ℎ)/(ℎ𝑥 (𝑥 + ℎ))〗 = lim┬(h→0)⁡〖ℎ/(ℎ𝑥 (𝑥 + ℎ))〗 = lim┬(h→0)⁡〖1/(𝑥 (𝑥 + ℎ))〗 Putting h = 0 = 1/(𝑥 (𝑥 + 0)) = 𝟏/𝒙𝟐

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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.