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Example 14 - Find derivative of f(x) = 1 + x + x2 + x3 .. + x50 - Derivatives by formula - x^n formula

Example 14 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Example 14 Find the derivative of f(x) = 1 + x + x2 + x3 +... + x50 at x = 1. We need to find f’ (x) at x = 1 i.e. f’ (1) f(x) = 1 + x + x2 + x3 +………. + x50 f’(x) = 1 + x + x2 + x3 +………. + x50﷯﷮′﷯ f’(x) = 0 + 1. x1-1 + 2x2-1 + 3x3-1 +………. + 50x50-1 = 1+ 2x + 3x2 +………. + 50x49 Hence , f’ (x) = 1 + 2x + 3x2 + … + 50x49 f’ (x) = 1 + 2x + 3x2 + … + 50x49 At x = 1 Putting x = 1 in f’(x) f’ (1) = 1 + 2 (1) + 3 (1)2 + ….. + 50 (1)49 = 1 + 2 + 3 +….. + 50 = 𝟓𝟎 (𝟓𝟎 + 𝟏)﷮𝟐﷯ = 50 (51)﷮2﷯ = 25 × 51 = 1275 Hence, f’(x) at x = 1 is 1275

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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.