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

Example 21 - Chapter 13 Class 11 Limits and Derivatives - Part 4
Example 21 - Chapter 13 Class 11 Limits and Derivatives - Part 5

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Transcript

Example 21 Compute derivative of (ii) g(x) = cot x g(x) = cot x = cos⁡𝑥/sin⁡𝑥 Let u = cos x & v = sin x ∴ g(x) = 𝑢/𝑣 So, g’(x) = (𝑢/𝑣)^′ Using quotient rule g’(x) = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 Finding u’ & v’ u = cos x u’ = – sin x & v = sin x v’ = cos x Now, f’(x) = (𝑢/𝑣)^′ = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑐𝑜𝑠⁡〖𝑥=〖− 𝑠𝑖𝑛 〗⁡𝑥 〗 ) (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑠𝑖𝑛⁡〖𝑥=〖𝑐𝑜𝑠 〗⁡𝑥 〗 ) = (−sin⁡〖𝑥 (sin⁡𝑥 ) −〖 cos〗⁡〖𝑥 (cos⁡〖𝑥)〗 〗 〗)/(〖𝑠𝑖𝑛〗^2 𝑥) = (−sin2⁡〖𝑥 −〖 cos2〗⁡〖𝑥 〗 〗)/(〖𝑠𝑖𝑛〗^2 𝑥) = (−(𝐬𝐢𝐧𝟐⁡〖𝒙 + 〖 𝐜𝐨𝐬𝟐〗⁡〖𝒙) 〗 〗)/(〖𝑠𝑖𝑛〗^2 𝑥) = (−𝟏)/(〖𝑠𝑖𝑛〗^2 𝑥) = –cosec2x Hence, f’(x) = –cosec2x (𝑈𝑠𝑖𝑛𝑔 𝑠𝑖𝑛2𝑥+𝑐𝑜𝑠2𝑥=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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.