**Table of content**

**NCERT Solutions for Class 12 Maths Chapter 5 – ****Continuity and Differentiability**

NCERT solutions for class 12 maths chapter 5 aimed at mastering the concepts and acquiring comprehensive knowledge about the various types of questions asked in examinations. In this NCERT Solution, all the questions provided with appropriate solutions will come in handy to revise the concept.

NCERT solutions for class 12 maths chapter 5 are prepared by our expert faculties to help you to prepare for your exams in a better way and enhance your score. We provide step by step solutions for the questions given in class 12 maths NCERT textbook as per CBSE Board guidelines. In case you have a doubt while you are studying, we have a team of teachers who prove live doubt solving session only for you.

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**CBSE Class 12 Maths Chapter 5 – ****Continuity and Differentiability NCERT Solutions**

In NCERT solutions for class 12 maths chapter 5, you will deal with continuity and differentiability, relations between them, differentiation of inverse trigonometric functions, exponential and logarithmic functions, different techniques of differentiation, certain geometrically conditions through differential calculus, some fundamental theorems.

**Sub-topics covered under NCERT Solutions for Class 12 Maths Chapter 5**

- 5.1 – Introduction
- 5.2 – Continuity
- 5.2.1 – Algebra of continuous functions
- 5.3 – Differentiability
- 5.3.1 – Derivatives of composite functions
- 5.3.2 – Derivatives of implicit functions
- 5.3.3 – Derivatives of inverse trigonometric functions
- 5.4 – Exponential and Logarithmic Functions
- 5.5 – Logarithmic Differentiation
- 5.6 – Derivatives of Functions in Parametric Forms
- 5.7 – Second Order Derivative
- 5.8 – Mean Value Theorem

In NCERT solutions for class 12 maths chapter 5, you will study about the algebra of continuous functions, differentiability derivatives of composite functions, implicit functions, inverse trigonometric functions, logarithmic differentiation, exponential and logarithmic functions, derivatives in parametric forms, mean value theorem. Let us now discuss the subtopics in detail

**NCERT Solutions for Class 12 Maths Chapter 5**

**5.1 – Introduction **

In this, you will study about the limit, differential, and continuity, their properties, methods to find derivatives by limits.

**5.2 – Continuity **

In this, you will learn about the continuity of a function at a given point i.e. a function is continuous if it is continuous on the whole of its domain, properties of a continuous function, types of discontinuity, intermediate value theorem, Cauchy’s definition, Heine’s definition.

**5.2.1 – Algebra of continuous functions **

In this, you learn if the function is continuous then its sum, difference, product, and quotient are also continuous.

**5.3 – Differentiability **

In this you will learn about the concept of differentiability – it is the change of quantity with respect to another quantity, standard differentiation, fundamental rules, types of derivatives, the relationship between continuity and differentiability.

**5.3.1 – Derivatives of composite functions **

In this, you will learn to find derivatives of composite function by left-hand limit and right-hand limit, chain rule.

**5.3.2 – Derivatives of implicit functions**

In this, you learn to find the derivatives of implicit functions its range, domain, principal value branch, graphs.

** 5.3.3 – Derivatives of inverse trigonometric functions **

In this, you will study about the derivatives of inverse trigonometric functions, its range, domain, principal value branch, graphs of inverse trigonometric functions, its elementary properties.

**5.4 – Exponential and Logarithmic Functions **

In this, you learn the concept of exponential and logarithmic functions i.e. differentiation of the exponential function and differentiation of the logarithmic functions.

**5.5 – Logarithmic Differentiation **

In this, you learn the concept of logarithmic differentiation i.e. differentiation of the function in the form of a logarithm.

**5.6 – Derivatives of Functions in Parametric Forms **

In this, you learn about derivatives of functions in parametric form.

**5.7 – Second Order Derivative **

In this, you will learn to differentiate the functions of second and third-order.

**5.8 – Mean Value Theorem**

In this section, you will state two fundamental results in calculus without proof, the geometric interpretation of theorems, Rolle’s Theorem, Mean Value Theorem.

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