Class 12 Math: Continuity and Differentiability Quick Revision Chapter Summary

Need to review the entire chapter before a test? This quick revision guide summarizes all the core concepts, topics, and equations taught in Class 12 Continuity and Differentiability to help you refresh your memory instantly.

Core Topics At a Glance

### 📌 Continuity checks A function is continuous at x = c if the limit as x approaches c exists and is equal to the function value f(c). Graphically, this means there is no break or jump in the curve.

### 📌 Differentiability criteria A function is differentiable at x = c if its tangent slope is well-defined. This requires the left-hand derivative (LHD) to equal the right-hand derivative (RHD) at that point.

### 📌 Chain rule of differentiation The chain rule calculates the derivative of a composite function. It states that the derivative of g(f(x)) is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

### 📌 Logarithmic differentiation Logarithmic differentiation is a technique used to differentiate functions of the form y = f(x)^g(x) or highly complex products. We take the natural logarithm of both sides to transform powers into products using log rules before differentiating.

### 📌 Second-order derivatives The second-order derivative is the derivative of the first derivative of a function. It measures the rate of change of the slope, representing acceleration in physics or concavity in geometry.

Key Formulas Mind Map

• Power Rule of Differentiation: `\frac{d}{dx}(x^n) = n x^{n-1}` - Differentiates exponential variable functions....
• The Chain Rule: `\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}` - Differentiates nested composite functions....

Revision Checklist

1. Review the subtopic guides and outline notes.
2. Practice writing the key formulas from memory.
3. Solve at least 3 worked examples and check your steps.
4. Take a timed practice quiz to verify your speed.