Derivative of log x
Understand the Problem
The question is asking for the derivative of the natural logarithm function, specifically ln(x). We will calculate the derivative using the rules of differentiation.
Answer
\frac{d}{dx}[\ln(x)] = \frac{1}{x}
Answer for screen readers
The derivative of ln(x) is 1/x
Steps to Solve
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Identify the function and apply the derivative rule for logarithms
We start with the function $f(x) = \ln(x)$. To find its derivative, we use the rule that the derivative of $\ln(x)$ is $\frac{1}{x}$. Therefore, the derivative of $f(x)$ is:
$$f'(x) = \frac{d}{dx}[\ln(x)] = \frac{1}{x}$$
The derivative of ln(x) is 1/x
More Information
The natural logarithm function is unique because its derivative is one of the simpler forms, which is part of why it's frequently used in calculus.
Tips
A common mistake is confusing the natural logarithm ln(x) with the common logarithm log(x) or assuming the derivative of ln(x) might involve more complex calculations. Remember that the derivative of ln(x) is straightforward: 1/x.
