Question

differentiate.
f(x)=\frac{1}{5x - 2}
f(x)=square

Explanation:

Step1: Rewrite the function

Rewrite $F(x)=\frac{1}{5x - 2}$ as $F(x)=(5x - 2)^{-1}$.

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 $u = 5x-2$, $\frac{du}{dx}=5$. So $F^\prime(x)=-1\cdot(5x - 2)^{-2}\cdot5$.

Step3: Simplify the result

$F^\prime(x)=-\frac{5}{(5x - 2)^2}$.

Answer:

$-\frac{5}{(5x - 2)^2}$