LOGARITHMIC DIFFERENTIATION


The following problems illustrate the process of logarithmic differentiation. It is a means of differentiating algebraically complicated functions or functions for which the ordinary rules of differentiation do not apply. For example, in the problems that follow, you will be asked to differentiate expressions where a variable is raised to a variable power. An example and two COMMON INCORRECT SOLUTIONS are : and

BOTH OF THESE SOLUTIONS ARE WRONG because the ordinary rules of differentiation do not apply. Logarithmic differentiation will provide a way to differentiate a function of this type. It requires deft algebra skills and careful use of the following unpopular, but well-known, properties of logarithms. Though the following properties and methods are true for a logarithm of any base, only the natural logarithm (base e, where e $ \approx 2.718281828 $), $ \ln $ , will be used in this problem set.


PROPERTIES OF THE NATURAL LOGARITHM


AVOID THE FOLLOWING LIST OF COMMON MISTAKES


The following problems range in difficulty from average to challenging.






Click HERE to return to the original list of various types of calculus problems.


Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address :

kouba@math.ucdavis.edu



Duane Kouba
1998-06-06