find the derivative.\ny = \\frac{7x + 6}{6x - 19};\ny =

Answer:

$y'=\frac{-161}{(6x - 19)^2}$

Explanation:

Step1: Apply quotient - rule

The quotient rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 7x+6$, $u'=7$, $v = 6x - 19$, $v'=6$.

Step2: Substitute values

$y'=\frac{7(6x - 19)-6(7x + 6)}{(6x - 19)^2}$

Step3: Expand numerator

$y'=\frac{42x-133-(42x + 36)}{(6x - 19)^2}=\frac{42x-133 - 42x-36}{(6x - 19)^2}$

Step4: Simplify numerator

$y'=\frac{-133 - 36}{(6x - 19)^2}=\frac{-161}{(6x - 19)^2}$