# Example 21

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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Example 21 Important You are here

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Class 11

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

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.