NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.5 Continuity and Differentiability
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.5 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 5.5.
Krati Saraswat29 Jan, 2024
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NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.5 Continuity and Differentiability
NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.5 Continuity and Differentiability is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of Chapter 5. Given below is step by step solutions of all questions given in NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.5 Continuity and Differentiability.NCERT Solutions for Class 12 Maths Chapter 5 Miscellaneous Exercise
NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.5 Overview
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.5 addresses these significant subjects. In order to fully comprehend the concepts presented in the chapter and make effective use of the provided solutions, it is recommended that students go over each topic in great detail. The intention is for students to effortlessly achieve excellent exam scores after reviewing and practicing these responses.NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.5
Solve The Following Questions NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.5 Continuity and Differentiability
Question 1. Differentiate the function with respect to x.cos x.cos 2x.cos3x
Solution : Let y = cos x.cos 2x.cos3x Taking logarithm on both the sides, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1
Question 2. Differentiate the function with respect to x.
Solution :
Let y =
Taking logarithm on both the sides, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.2
Question 3. Differentiate the function with respect to x.
Solution :
Let, y =
Taking logarithm on both the sides, we obtain
log y = cos x .log(log x)
Differentiating both sides with respect to x, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3
Question 4. Differentiate the function with respect to x.
Solution :
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.4
Question 5. Differentiate the function with respect to x.
Solution :
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.6
Question 6. Differentiate the function with respect to x.
Solution :
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7
Question 7. Differentiate the function with respect to x.
Solution :
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.8
Question 8. Differentiate the function with respect to x.
Solution :
Differentiating both sides with respect to x, we obtain
Question
9. Differentiate the function with respect to x.
Solution :
Let, y =
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
Question
10. Differentiate the function with respect to x.
Solution :
Let, y =
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
Question
11. Differentiate the function with respect to x.
Solution :
Let, y =
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
Question
12. Find dy/dx of function.
x
y
+ y
x
= 1
Solution :
The given function is x
y
+ y
x
= 1
Let x
y
= u and y
x
= v
Then, the function becomes u + v = 1
∴du/dx + dv/dx = 1
Differentiating both sides with respect to x, we obtain
Differentiating both sides with respect to x, we obtain
Question
13. Find dy/dx of function.
y
x
= x
y
Solution :
The given function is y
x
= x
y
Taking logarithm on both the sides, we obtain
x log y = y log x
Differentiating both sides with respect to x, we obtain
Question
14. Find dy/dx of function.
(cos x) y = (cos y) x
Solution : The given function is (cos x) y = (cos y) x Taking logarithm on both the sides, we obtain y log cos x = x log cos y Differentiating both sides, we obtain
Question
15. Find dy/dx of function.
xy = e (x-y)
Solution : The given function is xy = e (x-y) Taking logarithm on both the sides, we obtain log(xy) = log(e (x-y) ) Differentiating both sides with respect to x, we obtain
Question
16. Find the derivative of the function given by
and hence find f'(1)
Solution :
The given relationship is
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
Question
17. Differentiate
in three ways mentioned below
(i) By using product rule.
(ii) By expanding the product to obtain a single polynomial.
(iii By logarithmic differentiation.
Do they all give the same answer?
Solution :
Let, y =
(i)
(ii)
(iii) y =
Taking logarithm on both the sides, we obtain
Differentiating both sides with respect to x, we obtain
From the above three observations, it can be concluded that all the results of dy/dx are same.
Question
18. If u, v and w are functions of x, then show that
in two ways-first by repeated application of product rule, second by logarithmic differentiation.
Solution :
Let y = u.v.w = u(v.w)
By applying product rule, we obtain
By taking logarithm on both sides of the equation y = u.v.w, we obtain
log y = log u + log v + log w
Differentiating both sides with respect to x, we obtain
NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.5 FAQs
What is continuity in math class 12?
A real function (f) is said to be continuous if it is continuous at every point in the domain of f.
What is a continuous and differentiable function Class 12?
Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave. A differentiable function is a function whose derivative exists at each point in its domain.
How many exercises are there in chapter 5 class 12 maths?
There are total eight exercises and one misc exercise (144 Questions fully solved) in the class 12th maths chapter 5 Continuity and Differentiability.
What is the principle of continuity in math?
It is the principle that "whatever succeeds for the finite, also succeeds for the infinite".
What functions are not continuous?
Discontinuous functions are functions that are not a continuous curve - there is a hole or jump in the graph. It is an area where the graph cannot continue without being transported somewhere else.
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