Differentiability is an important topic in Class 12 Mathematics. It examines the existence of derivatives and the relationship between differentiability and continuity. A clear understanding of the definitions, conditions and standard methods is essential before attempting the chapter exercises.
These RD Sharma Solutions for Chapter 10, Differentiability, present a structured approach to questions involving Derivative from First Principles, Left Derivative, Right Derivative, Differentiability at a Point. Students can use the worked steps to identify the correct method, check intermediate calculations and strengthen problem-solving accuracy.
📌 Key Points to Remember
1Differentiability requires equal finite left and right derivatives
2Every differentiable function is continuous at that point
3A continuous function need not be differentiable
4Corners, cusps and vertical tangents require careful testing
🎯 Exam Tips for This Chapter
✓Check continuity before testing differentiability
✓Use the definition at piecewise joining points
✓Keep left and right increments consistent
✓Do not infer differentiability from continuity alone
📚 Topics Covered in This PDF
Derivative from First Principles
Left Derivative
Right Derivative
Differentiability at a Point
Continuity and Differentiability
Piecewise Functions
Absolute Value Functions
Composite Functions
❓ Frequently Asked Questions
What is the main idea of Differentiability?
It examines the existence of derivatives and the relationship between differentiability and continuity.
Which topics are covered in the Differentiability solutions?
The solutions cover Derivative from First Principles, Left Derivative, Right Derivative, Differentiability at a Point, Continuity and Differentiability, Piecewise Functions and related exercise problems.
What is the best way to solve questions from Differentiability?
Students should verify continuity, compute the left and right derivatives from the definition, and compare them.
Are these RD Sharma Solutions useful for the CBSE Class 12 board examination?
Yes. They provide detailed practice and help strengthen methods used in board-level questions. Students should follow the latest CBSE syllabus when selecting exercises.
Should students attempt the exercise before reading the solution?
Yes. An independent first attempt reveals conceptual gaps; the solution should then be used to check the method, calculations and final presentation.
Can the Differentiability solutions support competitive-exam preparation?
They can improve conceptual depth and calculation skill. Students should separately check the syllabus and question pattern of their target examination.
📖 About This Chapter
Differentiability forms part of the broader Class 12 Mathematics preparation and requires both conceptual clarity and regular written practice. This chapter focuses on Derivative from First Principles, Left Derivative, Right Derivative, Differentiability at a Point, Continuity and Differentiability, while the RD Sharma exercise set provides varied problems for reinforcing the methods. The solutions are useful for checking steps, locating calculation errors and comparing alternate approaches. Since RD Sharma may include material beyond the current board prescription, students should match the exercise topics with their latest school syllabus while using the additional questions for deeper practice.
