Lecture
Let function 
defined on interval 
.
Let the number 
. Give x increment Δx so that 
. Incrementing the argument Δx will cause the function to increment 
. The limit (if it exists) of the ratio of the increment of the function Δy to the increment of the argument Δx as Δx → 0 is called the derivative of the function and is denoted by 
i.e. 
At the same time, the function itself called differentiable .
The following symbols are also used to denote a derivative: 
.
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