NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 Continuity and Differentiability  PDF Download
JEE Mains & AdvancedNCERT solutions for class 12 maths chapter 5 exercise 5.7 Continuity and Differentiability focuses on secondorder derivatives and related concepts. The second derivative, also known as the secondorder derivative in calculus, is useful for calculating the rate of change of a quantity to itself. Ex 5.6 class 12 maths chapter 5 is a great way to assist students in applying a variety of methods to determine the secondorder derivatives of various function types.
Class 12 maths chapter 5 exercise 5.7 NCERT solutions consist of 17 questions based on derivatives. You can solve all the questions of exercise 5.7 with the help of NCERT solutions of ex 5.7 class 12 maths chapter 5 provided by the academic team of mathematics. Ex 5.7 class 12 maths ch 5 NCERT solution has explained the concept of second order derivatives to prepare for board exams. Class 12 maths chapter 5 exercise 5.7 NCERT solutions are also provided here in PDF format. You can download the free PDF of these solutions from the official website of eSaral and practice questions anytime.
Topics Covered in Exercise 5.7 Class 12 Mathematics Questions
Ex 5.7 class 12 maths chapter 5 covers the topic of second order derivatives. Students can check below the detailed explanation of this topic.
1. 
Second Order Derivative 

Second Order Derivative
The derivative of the function's first derivative is known as the second order derivative. We can determine the instantaneous rate of change of a function at a particular position or the slope of the tangent at that place using the firstorder derivative at that point. We can get an understanding of the shape of a graph for a particular function using the SecondOrder Derivative. The second order derivative of f(x) is denoted by f″(x). It is also denoted by D^{2} y or y″ or y_{2} if y = f(x).
Let y = f(x). Then
$\frac{d y}{d x}=f^{\prime}(x)$ ……(1)
If f′(x) is differentiable, we may differentiate (1) again w.r.t. x. Then, the left hand side becomes $\frac{d}{d x}\left(\frac{d y}{d x}\right)$ which is called the second order derivative of y w.r.t. x and is denoted by $\frac{d^2 y}{d x^2}$
Tips for Solving Exercise 5.7 Class 12 Chapter 5 Continuity and Differentiability
Our subject experts of eSaral have provided some useful tips to solve exercise 5.7 class 12 maths chapter 5.

While solving ex 5.7 class 12 maths NCERT solutions, students should remember that practicing examples is more important than just reading theory when they are preparing for board exams.

To acquire a more practical approach, you should also practice the important sums that are included in these solutions.

To prevent even the smallest errors, students must carefully follow each step of the solution.

Students will gain the necessary understanding of secondorder derivatives and their representation after closely reading the mathematical equations and solutions.
Importance of Solving Ex 5.7 Class 12 Maths Chapter 5 Continuity and Differentiability
There are numerous benefits of solving ex 5.7 class 12 maths chapter 5.

Second order derivatives included in exercise 5.7 have been described in detail by the expert teachers of eSaral that will help you to understand the nature of each question.

All the questions of ex 5.7 class 12 maths are solved in step by step manner which gives you clear and precise knowledge of concepts.

By practicing ex 5.7 class 12 maths chapter 5 in NCERT solutions will boost your selfconfidence to solve questions in board exams.

NCERT solution PDFs provide accurate answers to all the questions of ex 5.7 that will help you to cross check your answers.
Frequently Asked Questions
Since a function's secondorder derivative can only be found after its firstorder derivative has been determined, finding a function's secondorder derivative requires knowledge of how to find its firstorder derivative. Using the same techniques, you can find the secondorder derivative after you have the firstorder derivative. Finding both derivatives will be simpler for you if you are familiar with the fundamentals of differentiation.
If y = f(x). Then $\frac{d y}{d x}$= f ′(x) If f ′(x) is differentiable, we may differentiate $\frac{d y}{d x}$ again w.r.t. x. Then, the left hand side becomes $\frac{d}{d x}\left(\frac{d y}{d x}\right)$ which is called the second order derivative of y w.r.t. x and is denoted by $\frac{d^2 y}{d x^2}$ The second order derivative of f(x) is denoted by f″(x). It is also denoted by D^{2} y or y″ or y_{2 }if y = f(x).
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