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Example 7 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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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) = (π‘™π‘–π‘š)┬(β„Žβ†’0) 𝑓⁑〖(π‘₯ + β„Ž) βˆ’ 𝑓(π‘₯)γ€—/β„Ž Here, f(x) = sin x f(x + h) = sin (x + h) Now, f’(x) = lim┬(hβ†’0) 𝑠𝑖𝑛⁑〖(π‘₯ + β„Ž) βˆ’ 𝑠𝑖𝑛 π‘₯γ€—/β„Ž Putting x = 0 f’ (0) = lim┬(hβ†’0) 𝑠𝑖𝑛⁑〖(0 + β„Ž) βˆ’ 𝑠𝑖𝑛 (0)γ€—/β„Ž = lim┬(hβ†’0) sinβ‘γ€–β„Ž βˆ’ 0γ€—/h = lim┬(hβ†’0) sinβ‘γ€–β„Ž γ€—/h = 1 Hence, derivative of sin x at x = 0 is 1 Using lim┬(xβ†’0) sin⁑π‘₯/π‘₯ = 1 Replacing x by h lim┬(xβ†’0) sinβ‘β„Ž/β„Ž = 1

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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.