use the Leibniz notation δx and δy for changes or increments in the variables x and y
use the notation δx/δy for the difference quotient [f(x+h)−f(x)]/h where y=f(x)
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)
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
define the derivative f′(x) as lim_h→0 [f(x+h)−f(x)]/h
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)
interpret the derivative as the instantaneous rate of change
interpret the derivative as the slope or gradient of a tangent line of the graph of y=f(x)
