Examples

Chapter 12 Class 11 Limits and Derivatives
Serial order wise

### Transcript

Example 21 Compute derivative of (ii) g(x) = cot x g(x) = cot x = cosβ‘π₯/sinβ‘π₯ Let u = cos x & v = sin x β΄ g(x) = π’/π£ So, gβ(x) = (π’/π£)^β² Using quotient rule gβ(x) = (π’^β² π£ βγ π£γ^β² π’)/π£^2 Finding uβ & vβ u = cos x uβ = β sin x & v = sin x vβ = cos x Now, fβ(x) = (π’/π£)^β² = (π’^β² π£ βγ π£γ^β² π’)/π£^2 (π·ππππ£ππ‘ππ£π ππ πππ β‘γπ₯=γβ π ππ γβ‘π₯ γ ) (π·ππππ£ππ‘ππ£π ππ π ππβ‘γπ₯=γπππ  γβ‘π₯ γ ) = (βsinβ‘γπ₯ (sinβ‘π₯ ) βγ cosγβ‘γπ₯ (cosβ‘γπ₯)γ γ γ)/(γπ ππγ^2 π₯) = (βsin2β‘γπ₯ βγ cos2γβ‘γπ₯ γ γ)/(γπ ππγ^2 π₯) = (β(π¬π’π§πβ‘γπ + γ ππ¨π¬πγβ‘γπ) γ γ)/(γπ ππγ^2 π₯) = (βπ)/(γπ ππγ^2 π₯) = βcosec2x Hence, fβ(x) = βcosec2x (ππ πππ π ππ2π₯+πππ 2π₯=1)

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.