# Example 22

Last updated at March 9, 2017 by Teachoo

Last updated at March 9, 2017 by Teachoo

Transcript

Example 22 Find the derivative of (i) x5 − cosx sinx Let f(x) = x5− cosx sinx Let u = x5 – cos x & v = sin x So, f(x) = 𝑢𝑣 ∴ f’(x) = 𝑢𝑣′ Using quotient rule f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = x5 – cos x u’ = 5. x5 – 1 – ( – sin x) = 5x4 + sin x v = sin x v’ = cos x Now, f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = (5x4 + sinx) sin x − cos x(x5 − cos x) sin2x = 5x4 sinx + sin 2x − cos x . x5 + cos2 xsin2 x = −x5 cosx + 5x4 sinx + 𝐬𝐢𝐧𝟐 𝐱 + 𝐜𝐨𝐬𝟐 𝐱 sinx2 = −x5 cosx + 5x4 sinx + 𝟏 sinx2 Thus, f’(x) = −𝐱𝟓 𝐜𝐨𝐬𝐱 + 𝟓𝐱𝟒 𝐬𝐢𝐧𝒙 + 𝟏 𝐬𝐢𝐧𝐱𝟐 Example 22 Find the derivative of (ii) 𝑥 + 𝑐𝑜𝑠𝑥 𝑡𝑎𝑛𝑥 Let f(x) = 𝑥 + 𝑐𝑜𝑠𝑥 𝑡𝑎𝑛𝑥 Let u = x + cos x & v = tan x ∴ f(x) = 𝑢𝑣 So, f’(x) = 𝑢𝑣′ Using quotient rule f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = x + cos x u’ = (x + cos x)’ = 1 – sin x v = tan x v’ = sec2x Now, f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = (𝟏− 𝐬𝐢𝐧𝒙) ( 𝐭𝐚𝐧𝒙) − 𝒔𝒆𝒄𝟐𝒙 (𝒙 + 𝐜𝐨𝐬𝒙) ( 𝐭𝐚𝐧𝒙)𝟐

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

Example 22 Important You are here

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.