Last updated at May 29, 2018 by Teachoo

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Misc 30 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): 𝑥𝑠𝑖𝑛𝑛 𝑥 Let f(x) = 𝑥𝑠𝑖𝑛𝑛 𝑥 Let u = x & v = sinn x ∴ f(x) = 𝑢𝑣 So, f’(x) = 𝑢𝑣′ Using quotient rule f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = x u’ = (x)’ = 1 v = sinn x Let p = sin x v = pn By Leibnitz product rule v’ = (pn)’ p’ = n pn – 1 p’ Putting p = sin x = n sinn – 1 x (sin x)’ = n sinn – 1 x cos x Now, f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = 1 sin𝑛 𝑥 − 𝑛 𝑠𝑖𝑛𝑛−1𝑥 cos𝑥 (𝑥) (𝑠𝑖𝑛𝑛𝑥)2 = 𝑠𝑖𝑛𝑛𝑥 − 𝑥 (𝑛 𝑠𝑖𝑛𝑛−1𝑥 cos𝑥) (𝑠𝑖𝑛𝑛𝑥)2 = 𝑠𝑖𝑛𝑛−1𝑥 . sin𝑥 − 𝑥 (𝑛 𝑠𝑖𝑛𝑛−1𝑥 cos𝑥) (𝑠𝑖𝑛𝑛𝑥)2 = 𝑠𝑖𝑛𝑛−1𝑥 (sin𝑥 − 𝑛𝑥 . cos𝑥) 𝑠𝑖𝑛2𝑛𝑥 = sin𝑥 − 𝑛𝑥 cos𝑥 𝑠𝑖𝑛2𝑛𝑥 . 𝑠𝑖𝑛− 𝑛−1𝑥 = sin𝑥 − 𝑛𝑥 cos𝑥 𝑠𝑖𝑛(2𝑛 − 𝑛+1)𝑥 = sin𝑥 − 𝑛𝑥 cos𝑥 𝑠𝑖𝑛𝑛 + 1𝑥 Thus, f’(x) = 𝒔𝒊𝒏𝒙 − 𝒏𝒙 𝒄𝒐𝒔𝒙 𝒔𝒊𝒏𝒏 + 𝟏𝒙

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

Misc 1 Important

Misc 6 Important

Misc 9 Important

Misc 24 Important

Misc 27 Important

Misc 28 Important

Misc 30 Important You are here

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

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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.