Derivatives of Exponential Functions

Proposition (Derivatives of Exponential Functions) The derivative of the exponential function is In the special case when we have and So,

        

Example (Derivatives of Exponential Functions) Find the equation of the tangent line to the function at

    Solution. Using the product rule, the derivative of   is



and so



The equation of the tangent line has slope



and so we have and with the point and thus,  



Therefore, an equation of the tangent line is



Here is an illustration of the graph of and the tangent line:

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Derivatives Of Exponential Functions
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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