Example 19 (ii) - Chapter 12 Class 11 Limits and Derivatives

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Transcript

Example 19 Find the derivative of f from the first principle, where f is given by (ii) f(x) = x + 1/x Given f (x) = x + 1/x We need to find Derivative of f(x) i.e. f’ (x) We know that f’(x) = lim┬(hβ†’0) 𝑓⁑〖(π‘₯ + β„Ž) βˆ’ 𝑓(π‘₯)γ€—/β„Ž Here, f(x) = x + 1/x f(x + h) = (x + h) + 1/(x + β„Ž) Putting values f’(x) = lim┬(hβ†’0)⁑〖(((π‘₯ + β„Ž)+ 1/(π‘₯ + β„Ž)) βˆ’ (π‘₯ + 1/π‘₯))/hγ€— = lim┬(hβ†’0)⁑〖(π‘₯ + β„Ž+ 1/(π‘₯ + β„Ž) βˆ’ π‘₯ βˆ’ 1/(π‘₯ ))/hγ€— = lim┬(hβ†’0)⁑〖(β„Ž+ 1/(π‘₯ + β„Ž) βˆ’ 1/π‘₯ + π‘₯ βˆ’ π‘₯)/β„Žγ€— = lim┬(hβ†’0)⁑〖(β„Ž+ 1/(π‘₯ + β„Ž) βˆ’ 1/π‘₯)/β„Žγ€— = lim┬(hβ†’0)⁑〖(β„Ž+ (π‘₯ βˆ’ (π‘₯ βˆ’ β„Ž))/((π‘₯ + β„Ž) (π‘₯)))/β„Žγ€— = lim┬(hβ†’0)⁑〖(β„Ž + ((βˆ’β„Ž))/((π‘₯ + β„Ž) π‘₯))/β„Žγ€— = lim┬(hβ†’0)⁑〖( β„Ž(1 βˆ’ 1/((π‘₯ + β„Ž) π‘₯)))/β„Žγ€— = lim┬(hβ†’0)⁑(1βˆ’1/((π‘₯ + β„Ž) π‘₯)) Putting h = 0 = [1βˆ’1/(π‘₯ (π‘₯ + 0) )] = πŸβˆ’πŸ/(π’™πŸ )

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo