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- Jan 26, 2012
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Define the derivative of the natural logarithm to be: \(\displaystyle \frac{d}{dx} \ln(x) = \frac{1}{x}\)
Demonstrate this rule is valid by using the limit definition of a derivative.
Hint:
This definition of the exponential function is necessary to calculate the limit.
\(\displaystyle e^x = \lim_{n \to \infty} \left({1 + \frac x n}\right)^n\)
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Demonstrate this rule is valid by using the limit definition of a derivative.
Hint:
This definition of the exponential function is necessary to calculate the limit.
\(\displaystyle e^x = \lim_{n \to \infty} \left({1 + \frac x n}\right)^n\)
Remember to read the POTW submission guidelines to find out how to submit your answers!