Download Free PDF of Continuity and Differentiability Exercise 5.7 for Class 12 Maths
FAQs on CBSE Class 12 Mathematics Chapter 5 Continuity and Differentiability – NCERT Solutions 2025-26
1. How do I apply the chain rule in question 3 of Exercise 5.7?
The chain rule in Class 12 Maths Chapter 5 Exercise 5.7 lets you find derivatives of composite functions stepwise.
To apply the chain rule:
- Identify the outer function and inner function in the given expression.
- Differentiate the outer function, keeping the inner function as it is.
- Multiply by the derivative of the inner function.
- Simplify thoroughly and match each step to the NCERT solution pattern.
2. Which formulas are most important for Continuity and Differentiability in Class 12 CBSE?
The most important formulas for Chapter 5 are those frequently used in board and NCERT exercises.
Key formulas include:
- Chain Rule: d/dx [f(g(x))] = f'(g(x)) · g'(x)
- Derivative of inverse trigonometric functions: e.g., d/dx [sin-1x] = 1/√(1-x2)
- Implicit Differentiation technique
- Derivatives of exponential and logarithmic functions
- Standard derivatives for all trigonometric functions
3. What is the stepwise process for solving implicit differentiation questions in Ex 5.7?
To solve implicit differentiation questions in NCERT Exercise 5.7:
Follow these steps:
- Differentiate both sides of the equation with respect to x.
- Treat y as an implicit function: apply chain rule when differentiating terms with y.
- Whenever you differentiate y, multiply the result by dy/dx.
- Collect all terms containing dy/dx on one side of the equation and move other terms to the opposite side.
- Solve for dy/dx to get the required derivative.
4. Can I download the solutions for Exercise 5.7 as a PDF for offline study?
Yes, you can download the complete NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 as a PDF for offline revision.
Benefits of downloading the PDF:
- Access stepwise, CBSE-aligned answers anytime
- Easy last-minute revision for board exams
- Better clarity with highlighted formulas and detailed explanations
5. How does Vedantu ensure all solutions are CBSE board exam-compliant?
Vedantu guarantees board exam compliance in Class 12 Maths Ex 5.7 solutions through several measures:
- Mapping all solutions to the latest CBSE/NCERT syllabus (2025)
- Stepwise answers as per CBSE marking scheme
- Peer review by expert Mathematics faculty and recent toppers
- Regular updates for accuracy and syllabus changes
6. How to score maximum marks in derivatives chapter for the board exam?
To score full marks in the derivatives chapter (Continuity and Differentiability):
Follow these steps:
- Practice all NCERT solved examples and Exercise 5.7 solutions step-by-step
- Memorise critical formulas and understand their application
- Write each derivative and algebraic step clearly—no skips
- Use proper mathematical reasoning for chain rule and implicit differentiation
- Review CBSE previous years' questions for exam-trending patterns
7. What topics are covered in NCERT Class 12 Maths Chapter 5 Exercise 5.7?
NCERT Class 12 Maths Chapter 5 Exercise 5.7 covers key differentiability topics required for board exams:
- Chain rule application for composite functions
- Implicit differentiation
- Derivatives of inverse trigonometric and exponential functions
- Error-checking and stepwise algebraic manipulation
8. How many exercises are in continuity and differentiability class 12?
There are typically 7 main exercises plus a miscellaneous exercise in Chapter 5 (Continuity and Differentiability) of NCERT Class 12 Maths.
- Each exercise focuses on a specific concept: basic derivatives, chain rule, implicit differentiation, and more.
- Exercise 5.7 practises advanced differentiation methods crucial for the board exam.
9. Why use stepwise NCERT Solutions for Exercise 5.7 instead of shortcuts?
Using stepwise NCERT Solutions for Exercise 5.7 ensures you:
- Gain clear understanding of core concepts like chain rule and implicit differentiation
- Match every mark in the CBSE board exam's scheme
- Reduce errors and improve answer writing skills
- Score higher as steps are explicitly marked, not just final answers
10. Which CBSE board exams and entrance tests is Continuity and Differentiability relevant for?
Continuity and Differentiability (Class 12, Chapter 5) is important for:
- CBSE Board exam (high calculus weightage, regular board questions)
- NEET (medical entrance, calculus section)
- JEE Main (engineering entrance, concept and application based)
11. What is the LCD in math class 12?
In Class 12 Maths, LCD stands for Lowest Common Denominator. It is mainly used to add or subtract rational expressions by expressing them with the same denominator.
- It is not the primary focus of Chapter 5 (Continuity and Differentiability), but knowing the LCD helps simplify expressions while differentiating fractions.
12. How to check continuity class 12?
To check continuity in Class 12 Maths:
- Find the left hand limit (LHL), right hand limit (RHL), and the function value at the point of interest.
- If LHL = RHL = f(a), the function is continuous at x = a.











