Last updated at May 29, 2018 by Teachoo

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Ex 13.2, 9 Find the derivative of (i) 2 3 4 Let f(x) = 2 3 4 f (x) = (2 3 4 ) = 2 0 = 2 f (x) = 2 Ex 13.2, 9 Find the derivative of (ii) (5x3 + 3x 1) (x 1) Let f(x) = (5x3 + 3x 1) (x- 1) Let u = 5x3 + 3x 1 & v = x 1 f(x) = uv So, f (x) = (uv) f (x) = u v + v u Finding u & v u = 5x3 + 3x 1 u = 5.3x3 1 + 3.1.x1 1 0 = 15x2 + 3x0 = 15x2 + 3 v = x 1 v = 1 .x1 1 0 = 1. x0 = 1 f (x) = u v + v u = (15x2 + 3) (x 1) + (1) (5x3 + 3x 1) = 15x2 (x 1) + 3 (x 1) + 5x3 + 3x 1 = 15x3 15x2 + 3x 3 + 5x3 + 3x 1 = 15x3 + 5x3 15x2 + 3x + 3x 3 1 = 20x3 15x2 + 6x 4 Hence f (x) = 20x3 15x2 + 6x 4 Ex 13.2, 9 Find the derivative of (iii) x 3 (5 + 3x) Let f(x) = x 3 (5 + 3x) Let u = x 3 & v = 5 + 3x f(x) = uv So, f (x) = (uv) f (x) = u v + v u Finding u & v u = x 3 u = 3x 3 1 = 3x 4 v = 5 + 3x v = 0 + 3 = 3 Now, f (x) = (uv) = u v + v u = 3x 4 (5 + 3x) + 3 (x 3) = 15x 4 9x 4+ 1 + 3x 3 = 15x 4 6x 3 = 15 4 6 3 = 3 4 (5 + 2x) Hence f (x) = (5 + 2x) Ex 13.2,9 Find the derivative of (iv) x5 (3 6x 9 ). Let f (x) = x5 (3 6x 9 ) Let u = x5 & v = 3 6x 9 So, f(x) = uv f (x) = (uv) f (x) = u v + v u Finding u & v u = x5 u = 5x5 1 = 5x4 v = 3 6x 9 v = 0 6( 9)x 9 1 v = 54x 10 Now, f (x) = (uv) = u v + v u = 5x4 (3 6x 9) + 54x 10) (x5) = 15x4 30x 9 + 4 + 54 10 + 5 = 15x4 30x 5 + 54x 5 = 15x4 + 24x 5 = 15x4 + 24 5 Hence f (x) = 15x4 + Ex 13.2, 9 Find the derivative of (v) f (x) = x 4 (3 4x 5) Let f(x) = x 4 (3 4x 5) Let u = x 4 & v = 3 4x 5 f(x) = uv So, f (x) = (uv) f (x) = u v + v u Finding u & v u = x 4 u = 4x 4 1 = 4x 5 v = 3 4x 5 v = 0 4 ( 5) x 5 1 = 20x 6 Now, f (x) = (uv) = u v + v u = ( 4x 5 ) (3 4x 5) + (20x 6) (x 4) = 12x 5 + 16x 5 5 + 20 6 4 = 12x 5 + 16x 10 + 20x 10 = 12x 5 + 36x 10 = 12 5 + 36 10 Hence f (x) = + Ex 13.2, 9 Find the derivative of (vi) f(x) = 2 x + 1 x2 3x 1 Let f (x) = 2 x + 1 x2 3x 1 Let f1 (x) = 2 x + 1 & f2 (x) = x2 3x 1 f(x) = f1(x) f2 (x) So, f (x) = (f1(x) f2(x)) f (x) = f 1(x) f 2(x) Finding f1 (x) f1 (x) = 2 + 1 Let u = 2 & v = x + 1 f1(x) = Now, f1 (x) = f1 (x) = 2 u = 2 u = 0 v = x + 1 v = 1 + 0 = 1 f 1(x) = = 2 = 0 + 1 1 (2) + 1 2 = 2 ( + 1) 2 Hence, f1 (x) = 2 + 1 2 Finding f2 (x) f2 (x) = 2 3 1 Let u = x2 & v = 3x 1 f2 (x) = Now, f2 (x) = f2 (x) = 2 Finding u & v u = x2 u = 2x2 1 = 2x & v = 3x 1 v = 3(1) 0 = 3 f 2(x) = = 2 = 2 3 1 3 ( 2) 3 1 2 = 6 2 2 3 2 (3 1) 2 = 3 2 2 (3 1) 2 = (3 2) (3 1) 2 Hence f 2(x) = (3 2) 3 + 1 2 Now f (x) = f1 (x) f2 (x) = + ( ) ( )

Chapter 13 Class 11 Limits and Derivatives

Example 2
Important

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 You are here

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

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.