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RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each of the following functions: (i) x 3 + tan x Solution: (ii) Sin (log x) Solution:

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Page 1: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each of the following functions: (i) x3 + tan x Solution:

(ii) Sin (log x) Solution:

Page 2: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

(iii) Log (sin x) Solution:

Page 3: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

(iv) ex sin 5x Solution:

Page 4: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

(v) e6x cos 3x Solution: Let, y = e6x cos 3x

Page 5: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 6: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

(vi) x3 log x Solution:

Page 7: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

(vii) tan-1x Solution:

Page 8: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

(viii) x cos x Solution:

Page 9: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

(ix) Log (log x) Solution:

Page 10: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 11: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Hence proved.

Solution: Given y = x + tan x

Page 12: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 13: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 14: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 15: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Hence proved.

Solution:

Page 16: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 17: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 18: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 19: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 20: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 21: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 22: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 23: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 24: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 25: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 26: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 27: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Hence proved.

Page 28: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 29: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 30: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 31: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 32: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 33: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 34: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Solution:

Page 35: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives

Page 36: Exercise 12.1 Page No: 12 · RD Sharma Solutions for Class 12 Maths Chapter 12 Higher Order Derivatives Exercise 12.1 Page No: 12.17 1. Find the second order derivatives of the each

RD Sharma Solutions for Class 12 Maths Chapter 12

Higher Order Derivatives