# Example 21 - Chapter 13 Class 11 Limits and Derivatives

Last updated at July 11, 2019 by Teachoo

Last updated at July 11, 2019 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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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.