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Ex 13.2, 3 - Find derivative of x at x = 1 - Chapter 13 - Derivatives by 1st principle - At a point

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  1. Chapter 13 Class 11 Limits and Derivatives
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Ex 13.2, 3 Find the derivative of x at x = 1. Let f (x) = x We need to find derivative of f(x) at x = 1 i.e. f’ (1) We know that f’ (x) = lim﷮h→0﷯﷮ f x + h﷯−f (x)﷮h﷯﷯ Here, f(x) = x So, f(x + h) = x + h Putting values f’ (x) = lim﷮h→0﷯﷮ 𝑥 + ℎ﷯ − 𝑥﷮ℎ﷯﷯ = lim﷮h→0﷯﷮ 𝑥 − 𝑥 + ℎ﷮ℎ﷯﷯ = lim﷮h→0﷯﷮ ℎ﷮h﷯﷯ = lim﷮h→0﷯ 1 = 1 Hence, f’ (x) = 1 Putting x = 1 f’(1) = 1 So, derivative of x at x = 1 is 1

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