Example 21 (i) - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 21 Compute derivative of (i) f(x) = sin 2x Let f (x) = sin 2x = 2 sin x cos x Let u = 2 sin x & v = cos x So, f(x) = uv ∴ f’(x) = (uv)’ = u’v + v’u Here, u = 2 sin x u’ = 2 cos x & v = cos x v’ = – sin x f’(x) = (uv)’ = u’v + v’ u = 2 cos x . cos x + 2 sin x ( – sin x) = 2 cos2 x – 2 sin2 x = 2 (cos2 x – sin2 x) ∴ f’(x) = 2 (cos2 x – sin2 x) (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑠𝑖𝑛〖𝑥=𝑐𝑜𝑠𝑥 〗) (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑐𝑜𝑠〖𝑥=〖− 𝑠𝑖𝑛〗𝑥 〗)
Examples
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) You are here
Example 21 (ii) Important
Example 22 (i)
Example 22 (ii) Important
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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 and Computer Science at Teachoo