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Example 10 - Find derivative of f(x) = x2 - Chapter 13 Limits - Derivatives by 1st principle - At a general point

Example 10 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Example 10 Find the derivative of f(x) = x2. Given f(x) = x2 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) = x2 So, f (x + h) = (x + h)2 Putting values f’ (x) = lim﷮h→0﷯ 𝑥 + ℎ﷯2 − 𝑥2﷮ℎ﷯ = lim﷮h→0﷯ 𝑥2 + ℎ2 + 2𝑥ℎ − 𝑥2 ﷮ℎ﷯ = lim﷮h→0﷯ ℎ2 + 2𝑥ℎ − 𝑥2 + 𝑥2﷮ℎ﷯ = lim﷮h→0﷯ ℎ ℎ + 2𝑥﷯ + 0﷮ℎ﷯ = lim﷮h→0﷯ ℎ (ℎ + 2𝑥)﷮ℎ﷯ = lim﷮h→0﷯ h + 2x Putting h = 0 = 0 + 2x = 2x Hence f’(x) = 2x

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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.