differentiate the function.\ny = \\frac{14}{\\ln(x)}\ny =

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 14$ and $v=\ln(x)$.

Step2: Find $u'$ and $v'$

Since $u = 14$ (a constant), $u'=0$. And since $v=\ln(x)$, by the derivative formula of $\ln(x)$, $v'=\frac{1}{x}$.

Step3: Apply quotient - rule

Substitute $u = 14$, $u' = 0$, $v=\ln(x)$ and $v'=\frac{1}{x}$ into the quotient - rule formula. $y'=\frac{0\times\ln(x)-14\times\frac{1}{x}}{(\ln(x))^{2}}$.

Step4: Simplify the expression

$y'=-\frac{14}{x(\ln(x))^{2}}$.

Answer:

$-\frac{14}{x(\ln(x))^{2}}$