# How do you solve d/dx (ln x)?

Nov 29, 2016

$\frac{d}{\mathrm{dx}} \ln x = \frac{1}{x}$

#### Explanation:

A fundamentally import calculus result is that $\frac{d}{\mathrm{dx}} {e}^{x} = {e}^{x}$

Let $y = \ln x \iff x = {e}^{y}$

Differentiate wrt $y$
$\frac{\mathrm{dx}}{\mathrm{dy}} = {e}^{y}$ (using above result)
$\therefore \frac{\mathrm{dx}}{\mathrm{dy}} = x$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{x}$ (By the chain rule)