Example 21 - Chapter 13 Class 11 Limits and Derivatives - Part 3

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Example 21 - Chapter 13 Class 11 Limits and Derivatives - Part 4

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Example 21 - Chapter 13 Class 11 Limits and Derivatives - Part 5

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

Transcript

Example 21 Compute derivative of (ii) g(x) = cot x g(x) = cot x = cos⁑π‘₯/sin⁑π‘₯ Let u = cos x & v = sin x ∴ g(x) = 𝑒/𝑣 So, g’(x) = (𝑒/𝑣)^β€² Using quotient rule g’(x) = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 Finding u’ & v’ u = cos x u’ = – sin x & v = sin x v’ = cos x Now, f’(x) = (𝑒/𝑣)^β€² = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 (π·π‘’π‘Ÿπ‘–π‘£π‘Žπ‘‘π‘–π‘£π‘’ π‘œπ‘“ π‘π‘œπ‘ β‘γ€–π‘₯=γ€–βˆ’ 𝑠𝑖𝑛 〗⁑π‘₯ γ€— ) (π·π‘’π‘Ÿπ‘–π‘£π‘Žπ‘‘π‘–π‘£π‘’ π‘œπ‘“ 𝑠𝑖𝑛⁑〖π‘₯=γ€–π‘π‘œπ‘  〗⁑π‘₯ γ€— ) = (βˆ’sin⁑〖π‘₯ (sin⁑π‘₯ ) βˆ’γ€– cos〗⁑〖π‘₯ (cos⁑〖π‘₯)γ€— γ€— γ€—)/(〖𝑠𝑖𝑛〗^2 π‘₯) = (βˆ’sin2⁑〖π‘₯ βˆ’γ€– cos2〗⁑〖π‘₯ γ€— γ€—)/(〖𝑠𝑖𝑛〗^2 π‘₯) = (βˆ’(π¬π’π§πŸβ‘γ€–π’™ + γ€– πœπ¨π¬πŸγ€—β‘γ€–π’™) γ€— γ€—)/(〖𝑠𝑖𝑛〗^2 π‘₯) = (βˆ’πŸ)/(〖𝑠𝑖𝑛〗^2 π‘₯) = –cosec2x Hence, f’(x) = –cosec2x (π‘ˆπ‘ π‘–π‘›π‘” 𝑠𝑖𝑛2π‘₯+π‘π‘œπ‘ 2π‘₯=1)

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Davneet Singh
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.