The derivative is an instantaneous rate of change, defined by a limit. This course evaluates limits and differentiates polynomial and trigonometric functions.
The course follows the NCERT Class 11 Mathematics chapter Limits and Derivatives and has 3 lessons. Each lesson explains the ideas with worked examples and ends with practice questions and full answers. The numbers in every example and question are our own, so the lessons can be used alongside the textbook exercises.
- Limits, One-sided limits, the algebra of limits, the standard limit of (xⁿ − aⁿ)/(x - a), and trigonometric limits.
- Derivatives and the Rules of Differentiation, The derivative from first principles, derivatives of powers and trigonometric functions, and the product and quotient rules.
- Limits and Derivatives: Mixed Practice, Twelve original questions on limits and derivatives, with answers.
By the end you will be able to:
- Evaluate limits algebraically and with standard limits.
- Find one-sided limits.
- Differentiate from first principles.
- Apply the sum, product and quotient rules.