CBSE · Class 12 · Mathematics · Chapter 5
Continuity and Differentiability
Continuity, differentiability and derivatives.
Start chapterLessons in this chapter
- 1Continuity and Continuous FunctionsUnderstand when nearby inputs lead to the expected output, and use limits, graphs, and function rules to test continuity.
- 2Differentiability and the Chain RuleConnect derivatives to limiting slopes, understand why continuity is necessary, and differentiate functions built from several layers.
- 3Implicit and Inverse Trigonometric DifferentiationDifferentiate relationships that do not isolate y, then use that method to understand inverse trigonometric derivatives and their domains.
- 4Exponential and Logarithmic FunctionsExplore two inverse families of functions, understand their graphs and laws, and differentiate natural exponentials and logarithms.
- 5Logarithmic DifferentiationUse logarithms to untangle products and changing powers, then connect the method to familiar derivative rules.
- 6Derivatives in Parametric FormFollow two coordinates controlled by one parameter and obtain their slope without eliminating that parameter.
- 7Second Derivatives and Differential IdentitiesDifferentiate a derivative, then use repeated differentiation to explain equations connecting a function with its rates of change.
- 8Chapter Summary and PracticeConnect continuity, derivative methods, domains, and second derivatives through a complete chapter review and substantial mixed problems.