One very common mistake in computing the derivative of the exponential
f(x)=ex is to use the Power Rule
for derivatives, rather than the formula
f '(x)=ex.
To see why the Power Rule does not work, consider what the
resulting derivative would be, using the Power Rule:
f '(x)=x ex-1
(please keep in mind that this is incorrect).
Using the functions f(x)=ex and
f '(x)=x ex-1 in the
same applet as on the previous page,
it is easy to see that the values of this "derivative" do not give slopes
of tangent lines to the graph of f '(x):
How to use this applet
So be careful, when computing the derivative of an exponential function,
to use the correct formula:
if f(x)=ex
then f '(x)=ex
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