One very common mistake in computing the derivative of the exponential
*f*(*x*)=*e*^{x} is to use the Power Rule
for derivatives, rather than the formula
*f* '(*x*)=*e*^{x}.
To see why the Power Rule does *not* work, consider what the
resulting derivative would be, using the Power Rule:
*f* '(*x*)=*x e*^{x-1}
(please keep in mind that this is *incorrect*).
Using the functions *f*(*x*)=*e*^{x} and
*f* '(*x*)=*x e*^{x-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*)=*e*^{x}
then *f* '(*x*)=*e*^{x}

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