Derivatives of ln(x) and e^x

Posted: February 18, 2016 in Calculus: An Introduction, Differential Calculus, The Derivative
Tags: ,

Once students have a feel for calculating derivatives by limits of various functions, the same is done for ln(x) and e^x. Each of these show the importance of binomial expansion as that skill is once again necessary in understanding why things are as they are.

Derivative of ln(x)

Derivative(ln)

The derivative of ln(x) have many applications including logistic growth which we will see later this semester. We can, however, put this to work immediately by using it along with our knowledge of the product and quotient laws of logarithms. These are woven together nicely to determine the product and quotient rules of differential calculus.

The Euler constant “e” is also exploited in deriving the Rule of 72.

 

Derivative of e^x

Derivative(e^x)

 

Geometric Perspective of d(a^x)/dx

Derivative Exponential Function

To interact with the function above, click on d(a^x)dx.

Click the link provided to see two additional perspectives on the derivative of e^x.

 

Thanks for reading.

 

Reference

Courant, Richard., John, Fritz (1999).  Introduction to Calculus and Analytics: Classics of Mathematics. New York, NY:  Springer-Verlag Berlin Heidelberg.

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