Exploration: Exponential Functions and Their Derivatives

Part 4: How NOT to Compute the Derivative

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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):

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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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