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Find an equation of the line tangent to the graph of f at x=1. The following problems range in difficulty from average to challenging.Ĭlick HERE to see a detailed solution to problem 1.Ĭlick HERE to see a detailed solution to problem 2.Ĭlick HERE to see a detailed solution to problem 3.Ĭlick HERE to see a detailed solution to problem 4.Ĭlick HERE to see a detailed solution to problem 5.Ĭlick HERE to see a detailed solution to problem 6.Ĭlick HERE to see a detailed solution to problem 7.Ĭlick HERE to see a detailed solution to problem 8.Ĭlick HERE to see a detailed solution to problem 9. Though the following properties and methods are true for a logarithm of any base, only the natural logarithm (base e, where eĪVOID THE FOLLOWING LIST OF COMMON MISTAKES

It requires deft algebra skills and careful use of the following unpopular, but well-known, properties of logarithms. Logarithmic differentiation will provide a way to differentiate a function of this type. An example and two COMMON INCORRECT SOLUTIONS are :īOTH OF THESE SOLUTIONS ARE WRONG because 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. It is a means of differentiating algebraically complicated functions or functions for which the ordinary rules of differentiation do not apply. The following problems illustrate the process of logarithmic differentiation.