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# NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.2 Continuity and Differentiability - PDF Download

NCERT solutions for class 12 maths chapter 5 exercise 5.2 Continuity and Differentiability have combined questions related to differentiability of functions. Students will learn to find the derivatives of composite functions by solving the questions found in NCERT solutions for class 12 maths chapter 5 exercise 5.2. eSaral’s expert team of mathematics have developed these solutions precisely so that you can comprehend the questions and score good marks in exams.

Class 12 maths chapter 5 exercise 5.2 NCERT solutions have a total of 10 questions that illustrate the concept of finding derivatives of composite functions. These solutions make it easy for students to organize how they will prepare for the topic to score higher marks in exams. NCERT solutions for class 12 maths chapter 5 ex 5.2 are available here in PDF format to encourage practice of questions and enhance the confidence in students. You can download the PDF for free of cost from the official website of eSaral. These NCERT solution PDFs can also be downloaded from the link given below.

## Topics Covered in Exercise 5.2 Class 12 Mathematics Questions

Exercise 5.2 class 12 maths chapter 5 explains differentiability and derivatives of composite functions in NCERT solutions provided by eSaral.

 1 Differentiability Derivatives of composite functions
1. Differentiability

Let say f is a real function and c is a point in its domain. The derivative of f at c is defined by

$\lim _{h \rightarrow 0} \frac{f(c+h)-f(c)}{h}$

provided this limit exists. Derivative of f at c is denoted by f ′(c) or ( ( )) | c d f x dx . The function defined by

$f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

The process of finding derivatives of a function is called differentiation.

The following rules were established as a part of algebra of derivatives:

(1) (u ± v)′ = u′ ± v′

(2) (uv)′ = u′v + uv′ (Leibnitz or product rule)

(3) $\left(\frac{u}{v}\right)^{\prime}=\frac{u^{\prime} v-u v^{\prime}}{v^2}$ ,  wherever v ≠ 0 (Quotient rule).

Theorem 3: If a function f is differentiable at a point c, then it is also continuous at that point.

• Derivatives of composite functions

Origin of The composite function's derivative is known as the composite function. When a variable is also a function of the variable, the function is called a composite function. It is simple to find the derivative of these functions, using the derivative of the composite function formula.

Theorem 4: (Chain Rule) Let f be a real valued function which is a composite of two functions u and v ; i.e., f = v o u. Suppose t = u(x) and if both dtdx and dvdt exist, we have

$\frac{d f}{d x}=\frac{d v}{d t} \cdot \frac{d t}{d x}$

## Tips for Solving Exercise 5.2 Class 12 Chapter 5 Continuity and Differentiability

NCERT solutions for class 12 maths chapter 5 ex 5.2 have been prepared by experts of eSaral to help students develop their ability to find the derivative of composite function. There are some useful tips prepared by our subject experts to help you solve exercise 5.2 class 12 maths chapter 5.

1. Class 12 maths chapter 5 exercise 5.2 NCERT solutions are an easy resource of understanding all the rules, terms, and theorems included in this exercise. By solving the questions and examples provided in the class 12 maths ex 5.2.

2. There is a theorem related to chain rule which you must understand to solve questions associated with this rule.

3. To solve questions of ex 5.2, you need to comprehend the concepts of differentiability and derivatives of composite functions.

## Importance of Solving Ex 5.2 Class 12 Maths Chapter 5 Continuity and Differentiability

eSaral’s subject experts have provided a lot of benefits of solving questions of ex 5.2 class 12 maths chapter 5 Continuity and differentiability which you can check below.

1. Class 12 maths chapter 5 ex 5.2 has questions which are based on finding derivatives of composite functions. These concepts are explained in a detailed format to solve each question without confusion.

2. There are some important theorems related to derivatives of composite functions like chain rule. These theorems are solved and elaborated by experts of mathematics at eSaral that gives you a clear idea of the concepts to solve ex 5.2 questions.

3. You can also check NCERT solutions for class 12 maths chapter 5 ex 5.2 to revise the concepts and find step by step solutions for each question.

4. You will be confident to attempt any question in the exam from this chapter after solving questions in NCERT solutions class 12 maths chapter 5 ex 5.2.

5. Practicing questions in NCERT solutions will improve your time management and problem solving skills in exams.

Chain rule is a rule to differentiate composites of functions. If f = v o u, t = u (x) and if both dt/dx and dv/dt exist then $\frac{d f}{d x}=\frac{d v}{d t} \cdot \frac{d t}{d x}$