NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.4 Continuity and Differentiability
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.4 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 5.4.
Krati Saraswat27 Jan, 2024
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NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.4 Continuity and Differentiability
NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.4 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 are step-by-step solutions of all questions given in the NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.4 Continuity and Differentiability.NCERT Solutions for Class 12 Maths Chapter 5 Miscellaneous Exercise
NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.4 Overview
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.4 covers these important topics. Students are encouraged to review each topic thoroughly in order to fully understand the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the outcome of the dedicated effort that the Physics Wallah teachers have been doing to aid students in understanding the ideas covered in this chapter. After going over and rehearsing these responses, the goal is for students to easily score outstanding exam results.NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.4
Solve The Following Questions NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.4 Continuity and Differentiability:
Question 1. Differentiate the following w.r.t. x:
Solution :
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1
Question 2. Differentiate the following w.r.t. x:
Solution :
Let y =
By using the chain rule, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.2
Question 3. Differentiate the following w.r.t. x:
Solution :
Let y =
By using the chain rule, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3
Question 4. Differentiate the following w.r.t. x: sin (tan–1 e -x ) Solution : Let, y = sin (tan–1 e -x ) By using the chain rule, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.5
Question 5. Differentiate the following w.r.t. x: log(cos e x ) Solution : Let y = log(cos e x ) By using the chain rule, we obtain
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.6
Question 6. Differentiate the following w.r.t. x:
Solution :
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7
Question 7. Differentiate the following w.r.t. x:
Solution :
Let y =
NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.8
Question 8. Differentiate the following w.r.t. x: log(log x), x > 1 Solution : Let y = log (log x),x > 1 By using the chain rule, we obtain
Question
9. Differentiate the following w.r.t. x:
Solution :
Let y =
By using the quotient rule, we obtain
Question
10. Differentiate the following w.r.t. x:
Solution :
Let y =
By using the chain rule, we obtain
Solve The Following Questions.
Question 1. Differentiate the following w.r.t. x:
Solution :
Question
2. Differentiate the following w.r.t. x:
Solution :
Let y =
By using the chain rule, we obtain
Question
3. Differentiate the following w.r.t. x:
Solution :
Let y =
By using the chain rule, we obtain
Question
4. Differentiate the following w.r.t. x: sin (tan–1 e
-x
)
Solution :
Let, y = sin (tan–1 e
-x
)
By using the chain rule, we obtain
Question
5. Differentiate the following w.r.t. x: log(cos e
x
)
Solution :
Let y = log(cos e
x
)
By using the chain rule, we obtain
Question
6. Differentiate the following w.r.t. x:
Solution :
Question
7. Differentiate the following w.r.t. x:
Solution :
Let y =
Question
8. Differentiate the following w.r.t. x: log(log x), x > 1
Solution :
Let y = log (log x),x > 1
By using the chain rule, we obtain
Question
9. Differentiate the following w.r.t. x:
Solution :
Let y =
By using the quotient rule, we obtain
Question
10. Differentiate the following w.r.t. x:
Solution :
Let y =
By using the chain rule, we obtain
NCERT Solutions For Class 12 Maths Chapter 5 Exercise 5.4 FAQs
What is the important formula for continuity and Differentiability?
If a function f(x) is continuous across the interval [a, b] and differentiable across the interval (a, b), then there exists a point c in the interval [a, b] such that f′(c)=f(b)−f(a)b−a f ′ ( c ) = f ( b ) − f ( a ) b − a .
What is continuity and Differentiability summary?
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.
What are the 2 conditions for differentiability?
differentiability is when the slope of the tangent line equals the limit of the function at a given point. This directly suggests that for a function to be differentiable, it must be continuous, and its derivative must be continuous as well.
Does differentiability depend on continuity?
No, continuity does not imply differentiability. For instance, the function ƒ: R → R defined by ƒ(x) = |x| is continuous at the point 0, but it is not differentiable at the point 0
What is the basic of differentiability?
For a function to be differentiable at any point x=a in its domain, it must be continuous at that particular point but vice-versa is not always true.
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