![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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/1.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/2.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/3.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/4.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/5.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/6.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/7.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/8.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/9.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/10.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/11.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/12.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/13.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/14.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/15.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/16.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/17.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/18.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/19.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/20.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/21.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/22.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/23.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/24.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/25.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/26.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/27.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/28.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/29.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/30.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/31.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/32.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/33.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/34.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/35.jpg)
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](https://reader030.vdocument.in/reader030/viewer/2022040120/5e932b77c22a49675c70e244/html5/thumbnails/36.jpg)
RD Sharma Solutions for Class 12 Maths Chapter 12
Higher Order Derivatives