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Example 5 - Find derivative at x = 2 of f(x) = 3x - Examples

Example 5 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Example 5 Find the derivative at x = 2 of the function f(x) = 3x. f (x) = 3x We know that, f’(x) = lim﷮h→0﷯ f﷮ x+h﷯−f(x)﷯﷮h﷯ Now, f(x) = 3x So, f(x + h) = 3 (x + h) f’ (x) = lim﷮h→0﷯ 3﷮ x + h﷯ − 3 (x)﷯﷮h﷯ Putting x = 2 f’ (2) = lim﷮h→0﷯ 3﷮ 2 + h﷯ − 3 (2)﷯﷮h﷯ = lim﷮h→0﷯ 6 + 3ℎ − 6﷮h﷯ = lim﷮h→0﷯ 3ℎ + 0﷮h﷯ = lim﷮h→0﷯ 3ℎ﷮h﷯ = lim﷮h→0﷯ 3 = 3 Hence the derivative of the function f(x) at x = 2 is 3 i.e. f’(2) = 3

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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.