Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 7

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Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 8

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Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 9

  1. Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
  2. Serial order wise

Transcript

Ex 13.2, 11 Find the derivative of the following functions: (iv) cosec x Let f (x) = cosec x f(x) = 1/sin⁑π‘₯ Let u = 1 & v = sin x ∴ f(x) = 𝑒/𝑣 So, f’(x) = (𝑒/𝑣)^β€² Using quotient rule f’(x) = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 Finding u’ & v’ u = 1 u’ = 0 & v = sin x v’ = cos x Now, f’(x) = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 = (0 (sin⁑〖π‘₯) βˆ’γ€– cos〗⁑〖π‘₯ (1)γ€— γ€—)/(〖𝑠𝑖𝑛〗^2 π‘₯) (Derivative of constant function = 0) (Derivative of sin x = cos x) = (0 βˆ’ π‘π‘œπ‘  π‘₯)/(〖𝑠𝑖𝑛〗^2 π‘₯) = (βˆ’ π‘π‘œπ‘  π‘₯)/(〖𝑠𝑖𝑛〗^2 π‘₯) = (βˆ’ π‘π‘œπ‘  π‘₯)/sin⁑π‘₯ . 1/sin⁑π‘₯ = – cot x cosec x = – cosec x cot x Hence f’(x) = – cosec x cot x Using cot x = π‘π‘œπ‘ /sin⁑π‘₯ & 1/sin⁑π‘₯ = cosec x

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.