find the derivative of f(x) = 4 / (8x + 7). f(x) =

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{4}{8x + 7}$ as $f(x)=4(8x + 7)^{-1}$.

Step2: Apply the chain - rule

The chain - rule states that if $y = u^n$ and $u = g(x)$, then $\frac{dy}{dx}=n\cdot u^{n - 1}\cdot g'(x)$. Here $n=-1$, $u = 8x + 7$, and $g(x)=8x + 7$ with $g'(x)=8$. $f'(x)=4\times(-1)\times(8x + 7)^{-2}\times8$.

Step3: Simplify the expression

$f'(x)=-32(8x + 7)^{-2}=-\frac{32}{(8x + 7)^2}$.

Answer:

$-\frac{32}{(8x + 7)^2}$