# 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

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Example 22 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.