Editing Derivative (section)

===Step 1:  Description of Bottleneck===
Students have difficulties to use derivative to calculate the change of function value. They believe the derivative is a magic transformation of one formula into another, e.g. x² into  2x.  In case they know,  that  "derivative=slope",  they do not know what exactly the slope means, because they do not calculate  "change of function value=slope*change of argument value".

Desired learning outcome:  Students should understand that the change of function value is proportional to the change of argument value, and the derivative is exactly the proportionality factor. Students should be able to construct a triangle on the graph of a function to visually represent changes in function values and the corresponding slope (rate of change). 

Concrete  problems may be, for example:

* A) Given that f(1)=2 and f'(1)=3 students should be able to make an estimation of f(1,01) as f(1)+f'(1)*0,01=2.003
* B) Given the entities of function and entities of argument, decide on the entities of derivative. E.g. fuel price: Argument x is in Litre,  function f(x) is in Euro,  follows that the  derivative f'(x) is in Euro/Litre
* C) Given the text, which describes the rate of change, deduce a differential equation.  E.g. the population growth: Newborns are proportional to the population number leads to the equation dN/dt=C*N