# Rules of Differentiation: Derivative of a constant
function

### Erin Horst

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.

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