# Example 21

Last updated at Jan. 11, 2019 by Teachoo

Last updated at Jan. 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

Chapter 13 Class 11 Limits and Derivatives

Example 2
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Example 3 Important

Ex 13.1, 6 Important

Ex 13.1,10 Important

Ex 13.1, 13 Important

Ex 13.1, 16 Important

Ex 13.1, 22 Important

Ex 13.1, 25 Important

Ex 13.1, 28 Important

Ex 13.1, 30 Important

Ex 13.1, 32 Important

Ex 13.2, 9 Important

Ex 13.2, 11 Important

Example 20 Important

Example 21 Important You are here

Example 22 Important

Misc 1 Important

Misc 6 Important

Misc 9 Important

Misc 24 Important

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Misc 30 Important

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 9 years. He provides courses for Maths and Science at Teachoo.