Question

attempt 1: 10 attempts remaining. find the derivative. y = (7x + 7)/(6x - 17); y =

Explanation:

Step1: Apply quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y^\prime=\frac{u^\prime v - uv^\prime}{v^{2}}$. Here, $u = 7x + 7$, so $u^\prime=7$, and $v = 6x-17$, so $v^\prime = 6$.

Step2: Substitute into quotient - rule formula

$y^\prime=\frac{7(6x - 17)- (7x + 7)\times6}{(6x - 17)^{2}}$.

Step3: Expand the numerator

Expand $7(6x - 17)- (7x + 7)\times6$:
\[

$$\begin{align*} 7(6x - 17)- (7x + 7)\times6&=(42x-119)-(42x + 42)\\ &=42x-119 - 42x-42\\ &=-161 \end{align*}$$

\]
So, $y^\prime=\frac{-161}{(6x - 17)^{2}}$.

Answer:

$\frac{-161}{(6x - 17)^{2}}$