Derive the function ln(x/y) with respect to x
Answer
$\frac{1}{x}$
Step-by-step explanation
Problem
$\frac{d}{dx}\left(\ln\left(\frac{x}{y}\right)\right)$
1
The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
$\frac{1}{\frac{x}{y}}\cdot\frac{d}{dx}\left(\frac{x}{y}\right)$
Answer
$\frac{1}{x}$