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Example 21 (ii) - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
Last updated at March 22, 2023 by Teachoo
Examples
Example 1 (i)
Example 1 (ii)
Example 1 (iii)
Example 2 (i)
Example 2 (ii) Important
Example 2 (iii) Important
Example 2 (iv)
Example 2 (v)
Example 3 (i) Important
Example 3 (ii) Important
Example 4 (i)
Example 4 (ii) Important
Example 5
Example 6
Example 7 Important
Example 8
Example 9
Example 10 Important
Example 11
Example 12
Example 13 Important
Example 14
Example 15 Important
Example 16
Example 17 Important
Example 18
Example 19 (i) Important
Example 19 (ii)
Example 20 (i)
Example 20 (ii) Important
Example 21 (i)
Example 21 (ii) Important You are here
Example 22 (i)
Example 22 (ii) Important
Transcript
Example 21 Compute derivative of (ii) g(x) = cot x g(x) = cot x = cos𝑥/sin𝑥 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 (sin𝑥 ) −〖 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)
