Example 7 - Find derivative of sin x at x = 0 - Chapter 13 - Examples

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  1. Chapter 13 Class 11 Limits and Derivatives
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Example ,7 Find the derivative of sin x at x = 0. Let f(x) = sin x We know that f’(x) = lim﷮h→0﷯ f﷮ x + h﷯ − f(x)﷯﷮h﷯ f(x) = sin x f(x + h) = sin (x + h) Now, f’(x) = lim﷮h→0﷯ 𝑠𝑖𝑛﷮ 𝑥 + ℎ﷯ − 𝑠𝑖𝑛 𝑥﷯﷮ℎ﷯ f’(x) = lim﷮h→0﷯ 𝑠𝑖𝑛﷮ 𝑥 + ℎ﷯ − 𝑠𝑖𝑛 𝑥﷯﷮ℎ﷯ Putting x = 0 f’ (0) = lim﷮h→0﷯ 𝑠𝑖𝑛﷮ 0 + ℎ﷯ − 𝑠𝑖𝑛 (0)﷯﷮ℎ﷯ = lim﷮h→0﷯ sin﷮ℎ − 0﷯﷮h﷯ = lim﷮h→0﷯ sin﷮ℎ ﷯﷮h﷯ = 1 Hence the derivative of sin x at x = 0 is 1

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