Example 12 - Find derivative of f(x) = 1/x - Class 11 - Examples

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  1. Chapter 13 Class 11 Limits and Derivatives
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Example 12 Find the derivative of f(x) = 1﷮x﷯ f (x) = 1﷮𝑥﷯ We need to find Derivative of f(x) i.e. f’ (x) We know that f’(x) = lim﷮h→0﷯ f﷮ x + h﷯ − f(x)﷯﷮h﷯ Here, f (x) = 1﷮𝑥﷯ So, f (x + h) = 1﷮(𝑥 + ℎ)﷯ Putting values f’ (x) = lim﷮h→0﷯ 1﷮(𝑥 + ℎ)﷯ − 1﷮𝑥﷯﷮ℎ﷯ = lim﷮h→0﷯ 𝑥 − (𝑥 + ℎ)﷮𝑥 (𝑥 + ℎ)﷯﷮ℎ﷯ = lim﷮h→0﷯ 𝑥 − 𝑥 − ℎ﷮𝑥 𝑥 + ℎ﷯ ℎ﷯ = lim﷮h→0﷯ −ℎ﷮ℎ. 𝑥 (𝑥 + ℎ)﷯ = lim﷮h→0﷯ −1﷮𝑥 (𝑥 + ℎ)﷯ Putting h = 0 = −1﷮𝑥 (𝑥 + 0)﷯ = −1﷮ 𝑥﷮2﷯﷯ Hence f’(x) = −𝟏﷮ 𝒙﷮𝟐﷯﷯

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.