Question

differentiate. f(x)=\frac{1}{9x - 8} f(x)=\frac{-9}{(9x - 8)^2}

Explanation:

Step1: Rewrite the function

Rewrite $F(x)=\frac{1}{9x - 8}$ as $F(x)=(9x - 8)^{-1}$.

Step2: Apply the chain - rule

The chain - rule states that if $y = u^n$ and $u$ is a function of $x$, then $\frac{dy}{dx}=n\cdot u^{n - 1}\cdot\frac{du}{dx}$. Here, $n=-1$ and $u = 9x - 8$, $\frac{du}{dx}=9$. So $F'(x)=-1\cdot(9x - 8)^{-1 - 1}\cdot9$.

Step3: Simplify the result

$F'(x)=-\frac{9}{(9x - 8)^2}$.

Answer:

$F'(x)=-\frac{9}{(9x - 8)^2}$