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

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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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