Differentiating Constant Multipliers
If we have a function which is multiplied by a constant
we will see that its derivative is found by the
Constant Multiplier Rule
This follows easily from the product rule:
since the derivative of the constant
Example:
Suppose that
What we have seen tells
us that
This makes sense since the graph of
is a
straight line with slope 3.
Questions:
 Can you explain the relationship between these
two graphs?
 What can you infer from the fact that the derivative is
always positive?
 What can you infer from the fact that the derivative is
constant?


To understand the constant multiplier rule more generally,
remember that multiplying a function by a constant
either stretches or compresses the graph in the vertical
direction; that is, if
the graph is
streched by a factor of
This reflects the fact that
the rate of change of the function has been increased by a factor of
