find the derivative of the function. y = (7x - 1)/(6x + 7) the solution is y = .

Explanation:

Step1: Apply quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 7x-1$, $u'=7$, $v = 6x + 7$, and $v'=6$.

Step2: Substitute values into formula

$y'=\frac{7(6x + 7)-(7x - 1)\times6}{(6x + 7)^{2}}$.

Step3: Expand numerator

Expand $7(6x + 7)-(7x - 1)\times6$: $7(6x + 7)=42x+49$ and $(7x - 1)\times6 = 42x-6$. So, $y'=\frac{42x + 49-(42x - 6)}{(6x + 7)^{2}}$.

Step4: Simplify numerator

$42x + 49-(42x - 6)=42x + 49-42x + 6=55$. So, $y'=\frac{55}{(6x + 7)^{2}}$.

Answer:

$\frac{55}{(6x + 7)^{2}}$