# Example 21 - Chapter 13 Class 11 Limits and Derivatives

Last updated at March 9, 2017 by Teachoo

Last updated at March 9, 2017 by Teachoo

Transcript

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 So, u’ = 2 cos x & v = cos x So, v’ = – sin x f’(x) = (uv)’ = u’v + v’ u = 2cos x . cos x + 2sin x ( – sin x) = 2cos2 x – 2sin2 x = 2 (cos2 x – sin2 x) = 2 cos 2x ∴ f’(x) = 2 cos 2x 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) = 𝑢𝑣 So, g’(x) = 𝑢𝑣′ Using quotient rule g’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = cos x u’ = – sin x & v = sin x v’ = cos x Now, f’(x)= 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = − sin𝑥 sin𝑥 − cos𝑥 ( cos𝑥) 𝑠𝑖𝑛2𝑥 = − sin2𝑥 − cos2𝑥 𝑠𝑖𝑛2𝑥 = −( 𝐬𝐢𝐧𝟐𝒙 + 𝐜𝐨𝐬𝟐𝒙) 𝑠𝑖𝑛2𝑥 = −𝟏 𝑠𝑖𝑛2𝑥 = – cosec2x Hence, f’(x) = – cosec2x

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.