CBSE Class 12 Mathematics – Continuity and Differentiability

Chapter Overview

The chapter ‘Continuity and Differentiability’ deepens the understanding of differential calculus, building on the concepts learned in previous classes. It begins by defining continuity and its conditions, then moves to differentiability and its relationship with continuity. The chapter also introduces the chain rule, derivatives of implicit and inverse trigonometric functions, exponential and logarithmic functions, and higher-order derivatives. This knowledge is vital for solving real-world problems in physics, engineering, and other sciences.

Important Keywords

• Continuity: A function is continuous at a point if the left-hand limit, right-hand limit, and the value of the function at that point are equal.
• Differentiability: A function is differentiable at a point if its derivative exists at that point.
• Chain Rule: Used for finding the derivative of a composite function.
• Implicit Differentiation: Used when a function is not given explicitly.
• Logarithmic Differentiation: Taking log of both sides of an equation to simplify the differentiation process.
• Second-Order Derivative: The derivative of the first derivative of a function.