Question

differentiate the function.
y = \frac{1}{(6x - 1)^3}
\frac{dy}{dx}=\square

Explanation:

Step1: Rewrite the function

Rewrite $y=\frac{1}{(6x - 1)^3}$ as $y=(6x - 1)^{-3}$.

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, $n=-3$ and $u = 6x-1$, and $\frac{du}{dx}=6$.
So, $\frac{dy}{dx}=-3\cdot(6x - 1)^{-3 - 1}\cdot6$.

Step3: Simplify the expression

$\frac{dy}{dx}=-3\cdot6\cdot(6x - 1)^{-4}=-18(6x - 1)^{-4}=-\frac{18}{(6x - 1)^4}$.

Answer:

$-\frac{18}{(6x - 1)^4}$