Chapter 8: Differential Calculus
Learn the foundational concepts of differential calculus, including limits, derivatives, tangents, and optimization techniques to solve practical problems.
Unit 1: Limits
Understand the concept of limits and how they are used to analyze the behavior of functions.
Start UnitUnit 2: Use Limits to Define the Derivative of a Function
Learn how limits are used to define the derivative of a function and understand its importance in calculus.
Start UnitUnit 3: Differentiation of Functions from First Principles
Explore differentiation from first principles and how to derive the gradient of a function.
Start UnitUnit 4: Use the Specific Rules for Differentiation
Master the rules of differentiation, including product, quotient, and chain rules to solve complex problems.
Start UnitUnit 5: Find the Equations of Tangents to Functions
Learn to find the equations of tangents to curves at given points using differentiation.
Start UnitUnit 6: The Second Derivative
Explore the concept of the second derivative and its use in determining the concavity of functions.
Start UnitUnit 7: Sketch Cubic Graphs
Learn to sketch cubic functions by finding critical points, inflection points, and analyzing the behavior of the graph.
Start UnitUnit 8: Optimization and Rate of Change
Apply calculus to solve optimization problems and understand how to find rates of change in practical contexts.
Start Unit