HL AA – Differentiation
First Principles
sin, cos, ln, e
Inflexion Points
L'Hopitals
Tangents/Normals
Product/Quotient
Optimisation
Implicit differentiation
Chain Rule
Maximum/Minimum
Higher Orders
Differentiation Review
Traffic Light Coding for Unit
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Learning Outcomes
Understand the concept of a limit from a table or graph. |
Understand that the derivative is a gradient or rate of change function, and its notation. |
Understand when functions are increasing or decreasing. |
Simple derivatives by reducing the powers, e.g axn |
Find the equations of tangents and normals to functions. |
Derivatives of sinx, cosx, lnx, and ex. |
Use and understand the chain rule. |
Use and understand the product and quotient rules. |
Understand the concept of maximum and minimum points. |
Find the second derivative, and use this distinguishing between maximum and minimum points |
Finding points of inflexion. |
Using differentiation for solving optimization problems. |
Understand informally continuity and differentiability of a function at a point. |
Differentiate from first principles using the concept of a limit. |
Use differentiation for higher orders (greater than the second derivative). |
Evaluation of a limit using Maclaurin’s Series or l’Hopital’s rule, and the repeated use of l’Hopital’s rule. |
Use implicit differentiation for related rates of change and optimization problems. |