# How do you use the quotient rule to find the derivative of y=x/ln(x) ?

Aug 13, 2014

$y ' = \frac{\ln x - 1}{\ln x} ^ 2$

Explanation

Suppose,

$y = f \frac{x}{g} \left(x\right)$

Using Quotient Rule, which is

$y ' = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g \left(x\right)} ^ 2$

Similarly, following for the given problem $y = \frac{x}{\ln} x$ and differentiating with respect to $x$, yields

$y ' = \frac{\left(x\right) ' \left(\ln x\right) - x \left(\ln x\right) '}{\ln x} ^ 2$

$y ' = \frac{\ln x - x \cdot \frac{1}{x}}{\ln x} ^ 2$

$y ' = \frac{\ln x - 1}{\ln x} ^ 2$