Question

attempt 1: 10 attempts remaining. let f(x) = \frac{7}{4x + 8}. find f(x). f(x) =

Explanation:

Step1: Identify the quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 7$ and $v=4x + 8$.

Step2: Find the derivatives of $u$ and $v$

The derivative of a constant $u = 7$ is $u'=0$. The derivative of $v = 4x+8$ with respect to $x$ is $v'=4$.

Step3: Apply the quotient - rule

Substitute $u = 7$, $u'=0$, $v = 4x + 8$, and $v'=4$ into the quotient - rule formula:
\[

$$\begin{align*} f'(x)&=\frac{0\times(4x + 8)-7\times4}{(4x + 8)^{2}}\\ &=\frac{0 - 28}{(4x + 8)^{2}}\\ &=-\frac{28}{(4x + 8)^{2}} \end{align*}$$

\]

Answer:

$-\frac{28}{(4x + 8)^{2}}$