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Ex 13.2, 3 - Find derivative of 99x at x = 100 - Class 11

Ex 13.2, 3 - Chapter 13 Class 11 Limits and Derivatives - Part 2


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Ex 13.2, 3 Find the derivative of 99x at x = 100 Let f (x) = x We need to find derivative of f(x) at x = 100 i.e. f’ (100) We know that f’ (x) = (π‘™π‘–π‘š)┬(β„Žβ†’0)⁑〖(𝑓(π‘₯ + β„Ž) βˆ’ 𝑓 (π‘₯))/β„Žγ€— Here, f(x) = 99x So, f(x + h) = 99(x + h) = 99x + 99h Putting values f’ (x) = lim┬(hβ†’0)⁑〖((99π‘₯ +99β„Ž) βˆ’ 99π‘₯)/β„Žγ€— = lim┬(hβ†’0)⁑〖(99π‘₯ +99β„Ž βˆ’ 99π‘₯)/β„Žγ€— = lim┬(hβ†’0)⁑〖99β„Ž/β„Žγ€— = lim┬(hβ†’0) 99 = 99 Hence, f’(x) = 99 Putting x = 100 f’(100) = 99 So, derivative of 99x at x = 100 is 99

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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.