NCERT Solutions for Maths Class 12 Exercise 5.7

Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 5.7.

You can download the PDF of NCERT Books Maths Chapter 5 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 5.7.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.

NCERT Solutions for Maths Class 12 Exercise 5.1

NCERT Solutions for Maths Class 12 Exercise 5.2

NCERT Solutions for Maths Class 12 Exercise 5.3

NCERT Solutions for Maths Class 12 Exercise 5.4

NCERT Solutions for Maths Class 12 Exercise 5.5

NCERT Solutions for Maths Class 12 Exercise 5.6

NCERT Solutions for Maths Class 12 Exercise 5.7

 

Find the second order derivatives of the functions given in Questions 1 to 10.

Maths Class 12 Ex 5.7 Question 1.

x² + 3x + 2

Solution:

Let y = x² + 3x + 2

Maths Class 12 Ex 5.7 Question 2.

x²⁰ 

Solution:

Let y = x²⁰ 

 Maths Class 12 Ex 5.7 Question 3.

x . cos x

Solution:
Let y = x . cos x

Maths Class 12 Ex 5.7 Question 4.

log x

Solution:
Let y = log x

Maths Class 12 Ex 5.7 Question 5.

x³ log x

Solution:
Let y = x³ log x

Maths Class 12 Ex 5.7 Question 6.

e^x sin 5x

Solution:
Let y = e^x sin 5x

Maths Class 12 Ex 5.7 Question 7.

e^6x cos 3x

Solution:
y = e^6x cos 3x

Maths Class 12 Ex 5.7 Question 8.

tan^-1 x

Solution:

Let y = tan^-1 x

Maths Class 12 Ex 5.7 Question 9.

log (log x)

Solution:
Let y = log (log x)

Maths Class 12 Ex 5.7 Question 10.

sin (log x)

Solution:
Let y = sin (log x)

Maths Class 12 Ex 5.7 Question 11.

If y = 5 cos x – 3 sin x, prove that 

Solution:
We have, y = 5 cos x – 3 sin x

Hence proved.

Maths Class 12 Ex 5.7 Question 12.

If y = cos^-1 x, find d²y/dx² in terms of y alone.

Solution:
We have, y = cos^-1 x

Maths Class 12 Ex 5.7 Question 13.

If y = 3 cos (log x) + 4 sin (log x), show that x²y₂ + xy₁ + y = 0

Solution:
We have, y = 3 cos (log x) + 4 sin (log x)

Maths Class 12 Ex 5.7 Question 14.

Solution:

Maths Class 12 Ex 5.7 Question 15.

If y = 500e^7x + 600e^-7x, show that 

Solution:
We have, y = 500e^7x + 600e^-7x

Maths Class 12 Ex 5.7 Question 16.

Solution:
We have, e^y (x + 1) = 1

Maths Class 12 Ex 5.7 Question 17.

If y = (tan^-1 x)², show that (x² + 1)² y₂ + 2x(x² + 1) y₁ = 2

Solution:
We have, y = (tan^-1 x)²

Related Links:

NCERT Solutions for Maths Class 12 Exercise 5.1

NCERT Solutions for Maths Class 12 Exercise 5.2

NCERT Solutions for Maths Class 12 Exercise 5.3

NCERT Solutions for Maths Class 12 Exercise 5.4

NCERT Solutions for Maths Class 12 Exercise 5.5

NCERT Solutions for Maths Class 12 Exercise 5.6