NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3 Continuity and Differentiability - PDF Download

NCERT solutions for class 12 maths exercise 5.3 Continuity and Differentiability is designed to teach students about the differentiability of a few standardized functions, such as implicit and inverse trigonometric functions. Class 12 maths chapter 5 exercise 5.3 provides NCERT solutions for all the questions of ex 5.3. Students can go through these solutions for better understanding of these sums. Ex 5.3 class 12 maths chapter 5’s questions are solved by subject experts of eSaral that make students familiar with the concepts of derivatives of implicit and inverse trigonometric functions.

Ex 5.3 class 12 maths ch 5 has included 15 questions that are based on finding the answers of some derivatives of functions with simple and step by step methods. These solutions are also available in PDF format. With the help of these PDFs, you will get well-written answers and can complete your error-free learning to achieve the desired exam results. You can easily download the free PDF of NCERT solutions class 12 maths ex 5.3 by clicking on the link provided below and practice all the questions.

Topics Covered in Exercise 5.3 Class 12 Mathematics Questions

Ex 5.3 class 12 maths solutions covers derivatives of implicit functions and inverse trigonometric functions. Detailed explanation can be found below.

1. Derivatives of implicit functions

y = f(x) is the form in which we have been differentiating different functions up until now.

However, this type of expression is not required for functions all the time. For example, think about the following x and y relationships:

                           $\begin{aligned} x-y-\pi & =0 \\ x+\sin x y-y & =0\end{aligned}$

In the first case, we can rewrite the relationship as y = x - π by solving for y. There doesn't seem to be a simple solution to solve for y in the second case. However, in both scenarios, there is no question regarding y's dependence on x. When a relationship between x and y is expressed in a way that is easy to solve for y and write y = f(x), we say that y is given as an explicit function of x. In the latter case it is implicit that y is a function of x and we say that the relationship of the second type, above, gives function implicitly. 

2. Derivatives of inverse trigonometric functions

We note that inverse trigonometric functions are continuous functions, but we won't prove this. Here, we use chain rule to find derivatives of these functions

To find a complete explanation of derivatives of inverse trigonometric function in ex 5.3 class 12 maths chapter 5, you can download the NCERT textbook here.

Tips for Solving Exercise 5.3 Class 12 Chapter 5 Continuity and Differentiability

NCERT solutions for class 12 maths chapter 5 exercise 5.3 are very helpful in promoting the confidence of students through practice of questions by the tips provided below. 

1. You should first try to solve questions on your own to find out where you need more focus on concepts. This will help you to plan your study to learn concepts accordingly. 

2. Students would benefit from practicing the questions in these solutions thoroughly as it will help them to follow a methodical preparation strategy for in-depth studies. 

3. By following a simple pattern of questions provided by eSaral’s subject experts, this will help you to gradually acquire an understanding of complex questions. 

Importance of Solving Ex 5.3 Class 12 Maths Chapter 5 Continuity and Differentiability

Solving questions of exercise 5.3 class 12 maths chapter 5 will provide you numerous benefits. You can find some of the important benefits below for preparing for exams.

1. NCERT solutions class 12 maths chapter 5 ex 5.3 helps students to gain a conceptual understanding of derivatives of implicit and inverse trigonometric functions to solve exercise questions with ease.

2. Class 12 maths chapter 5 exercise 5.3 NCERT solutions provides not only the questions but their easy and step by step answers that helps you in preparing for board exams.

3. The PDF solutions provided by expert teachers of eSaral will also help you to cross check your answers.

4. Practicing questions and revising all the concepts of ex 5.3 builds self-confidence while solving questions in exams.

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