HL AA – Differentiation

First Principles

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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.