## Derivative of ln(x)

Again, this is another post for my own amusement/memory

The derivative of $log_e(x)$ is $\frac{1}{x}$ – but I could find no proof for that online, so I worked out my own (admittedly this is not a complex problem).

Let $y=e^x$, then $x=log_e(y)$

We know $\frac{dy}{dx} = e^x$ so $\frac{dx}{dy} = \frac{d}{dy}log_e(y) = \frac{1}{e^x} =\frac{1}{y}$

Hence, to restate this in the standard manner $\frac{d}{dx}ln(x) = \frac{1}{x}$

### One response to “Derivative of ln(x)”

1. […] again we start from the proposition that there exists a number such that and hence (see here for why the second follows from the […]