attempt 1: 2 attempts remaining. let f(x)=6/(7x + 7). f(x)= submit answer next item

Explanation:

Step1: Recall quotient - rule

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

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

Since $u = 6$ (a constant), $u'=0$. And since $v = 7x+7$, $v'=7$.

Step3: Apply the quotient - rule

$f'(x)=\frac{0\times(7x + 7)-6\times7}{(7x + 7)^{2}}$.

Step4: Simplify the expression

$f'(x)=\frac{- 42}{(7x + 7)^{2}}=\frac{-42}{49(x + 1)^{2}}=\frac{-6}{7(x + 1)^{2}}$.

Answer:

$-\frac{6}{7(x + 1)^{2}}$