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9.03 Differentiation from first principles

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Outcomes

2.3.2

use the Leibniz notation δx and δy for changes or increments in the variables x and y

2.3.3

use the notation δx/δy for the difference quotient [f(x+h)−f(x)]/h where y=f(x)

2.3.4

interpret the ratios [f(x+h)−f(x)]/h and δy/δx as the slope or gradient of a chord or secant of the graph of y=f(x)

2.3.5

examine the behaviour of the difference quotient [f(x+h)−f(x)] / h as h→0 as an informal introduction to the concept of a limit

2.3.6

define the derivative f′(x) as lim_h→0 [f(x+h)−f(x)]/h

2.3.7

use the Leibniz notation for the derivative: dy/dx=lim_δx→0 δy/δx and the correspondence dy/dx=f′(x) where y=f(x)

2.3.8

interpret the derivative as the instantaneous rate of change

2.3.9

interpret the derivative as the slope or gradient of a tangent line of the graph of y=f(x)

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