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Exploration: Exponential Functions and Derivatives - How NOT to Compute the Derivative

Author(s): 
Tom Leathrum

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

Tom Leathrum, "Exploration: Exponential Functions and Derivatives - How [i]NOT[/i] to Compute the Derivative," Loci (October 2004)

JOMA

Journal of Online Mathematics and its Applications

Dummy View - NOT TO BE DELETED