Math formulae are used to describe (using symbols) the relationships in an observation.
They only describe the operations, it is wrong to say that the " ... operation is controlled by a set of ..."
Often one will plot out on graph paper the results of the experiment and then to see which math expression fits the data. Then try and explain why that expression is relevant.
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Fahrenheit = (Celsius * 1.8) + 32 Celsius = (Fahrenheit - 32) / 1.8
There are many uses in mathematics for derivative rules in order to derive from formulas. The main use of using derivative rules for mathematical formulas is to differentiate the logarithm.
You try to work out a pattern with the number of movements. You then turn your rule into an algebraic form eg. 2n + 3 (this is not the answer to the investigation but it might help.
I derive that this question needs to be moved.
The noun forms of the verb to derive are deriver, derivation, derivative, and the gerund, deriving.