Now that we have explored derivatives, we can now progress to the rules of differentiation. These rules are simply formulas that instruct the learner how to compute derivatives depending on a given function.
The simplest function is a constant function, which is also the simplest derivative to compute. The differentiation rule for a constatnt function is
(This differentiation rule is derived from the power rule.)
Now, consider why this might be true. Since the derivative is the slope of the function at any given point, then the slope of a constant function is always 0. Hence, the derivative of a constant function is always 0. Below are some illustrations of constant functions and their respective derivatives.
The following graph illustrates the function y=5 and its derivative y'=0.
The following graph illustrates the function y=-1 and its derivative y'=0.