Ex 12.2, 2 - Chapter 12 Class 11 Limits and Derivatives

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Ex 13.2, 2 - Find derivative of x at x = 1 - Class 11 Limits Ex 13.2, 2 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Ex 12.2, 2 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) = (π‘™π‘–π‘š)┬(β„Žβ†’0)⁑〖(𝑓(π‘₯ + β„Ž) βˆ’ 𝑓 (π‘₯))/β„Žγ€— Here, f(x) = x So, f(x + h) = x + h Putting values f’ (x) = lim┬(hβ†’0)⁑〖((π‘₯ + β„Ž) βˆ’ π‘₯)/β„Žγ€— = lim┬(hβ†’0)⁑〖(π‘₯ + β„Ž βˆ’ π‘₯)/β„Žγ€— = lim┬(hβ†’0)β‘γ€–β„Ž/β„Žγ€— = lim┬(hβ†’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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo