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Define the derivative of the natural logarithm to be: [math]\frac{d}{dx} \ln(x) = \frac{1}{x}[/math]
Demonstrate this rule is valid by using the limit definition of a derivative.
Hint:
[sp]
This definition of the exponential function is necessary to calculate the limit.
[math]e^x = \lim_{n \to \infty} \left({1 + \frac x n}\right)^n[/math]
[/sp]
Remember to read the http://www.mathhelpboards.com/threads/773-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
Demonstrate this rule is valid by using the limit definition of a derivative.
Hint:
[sp]
This definition of the exponential function is necessary to calculate the limit.
[math]e^x = \lim_{n \to \infty} \left({1 + \frac x n}\right)^n[/math]
[/sp]
Remember to read the http://www.mathhelpboards.com/threads/773-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!