What is the derivative of $f(x) = log(x)$? This post tries to prove that it is $\frac{1}{x}$ when the log base is $e$.
Derivative of exponential function and the definition of e
Before talking about the derivative of log function, let us review the definition of $e$. It is related to the derivative of the exponential function, for example, $f(x) = 2^x$.
According to the definition of derivative, we know that the derivative of $f(x) = …